Relevant bibliographies by topics / Local approximation of a function

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Academic literature on the topic 'Local approximation of a function'

Author: Grafiati
Published: 25 May 2024

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Journal articles on the topic "Local approximation of a function"

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Pal, Mahendra Kumar, M. L. L. Wijerathne, and Muneo Hori. "Numerical Modeling of Brittle Cracks Using Higher Order Particle Discretization Scheme–FEM." International Journal of Computational Methods 16, no. 04 (May 13, 2019): 1843006. http://dx.doi.org/10.1142/s0219876218430065.

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Higher order extension of Particle Discretization Scheme (HO-PDS), its implementation in FEM framework (HO-PDS-FEM) and applications in efficiently simulating cracks are presented in this paper. PDS is an approximation scheme which uses a conjugate domain tessellation pair like Voronoi and Delaunay in approximating a function and its derivatives. In approximating a function (or derivatives), HO-PDS first produces local polynomial approximations for the target function (or derivatives) within each element of respective tessellation. The approximations over the whole domain are then obtained by taking the union of those respective local approximations. These approximations are inherently discontinuous along the boundaries of the respective tessellation elements since the support of the local approximations is confined to the domain of respective tessellation elements and no continuity conditions are enforced. HO-PDS-FEM utilizes these inherent discontinuities in function approximation to efficiently model discontinuities such as cracks. Higher order PDS is implemented in FEM framework to solve boundary value problem of elastic solids, including mode-I crack problems. With several benchmark problems, it is shown that HO-PDS-FEM has higher expected accuracy and convergence rate. J-integral around a mode-I crack tip is calculated to demonstrate the improvement in the accuracy of the crack tip stress field. Further, it is shown that HO-PDS-FEM significantly improves the traction along the crack surfaces, compared to the zeroth-order PDS-FEM [Hori, M., Oguni, K. and Sakaguchi, H. [2005] “Proposal of FEM implemented with particle discretization scheme for analysis of failure phenomena,” J. Mech. Phys. Solids 53, 681–703].
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Fan, Jiang, Qinghao Yuan, Fulei Jing, Hongbin Xu, Hao Wang, and Qingze Meng. "Adaptive Local Maximum-Entropy Surrogate Model and Its Application to Turbine Disk Reliability Analysis." Aerospace 9, no. 7 (June 30, 2022): 353. http://dx.doi.org/10.3390/aerospace9070353.

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The emerging Local Maximum-Entropy (LME) approximation, which combines the advantages of global and local approximations, has an unsolved issue wherein it cannot adaptively change the morphology of the basis function according to the local characteristics of the sample, which greatly limits its highly nonlinear approximation ability. In this research, a novel Adaptive Local Maximum-Entropy Surrogate Model (ALMESM) is proposed by constructing an algorithm that adaptively changes the LME basis function and introduces Particle Swarm Optimization to ensure the optimality of the adaptively changed basis function. The performance of the ALMESM is systematically investigated by comparison with the LME approximation, a Radial basis function, and the Kriging model in two explicit highly nonlinear mathematical functions. The results show that the ALMESM has the highest accuracy and stability of all the compared models. The ALMESM is further validated by a highly nonlinear engineering case, consisting of a turbine disk reliability analysis under geometrical uncertainty, and achieves a desirable result. Compared with the direct Monte Carlo method, the relative error of the ALMESM is less than 1%, which indicates that the ALMESM has considerable potential for highly nonlinear problems and structural reliability analysis.
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Chen, Yuanqiang, H. Zheng, Wei Li, and Shan Lin. "MLS based local approximation in numerical manifold method." Engineering Computations 35, no. 7 (October 1, 2018): 2429–58. http://dx.doi.org/10.1108/ec-12-2017-0485.

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Purpose The purpose of this paper is to propose a new three-node triangular element in the framework of the numerical manifold method (NMM), which is designated by Trig3-MLScns. Design/methodology/approach The formulation uses the improved parametric shape functions of classical triangular elements (Trig3-0) to construct the partition of unity (PU) and the moving least square (MLS) interpolation method to construct the local approximation function. Findings Compared with the classical three-node element (Trig3-0), the Trig3-MLScns element has a higher order of approximations, much better accuracy and continuous nodal stress. Moreover, the linear dependence problem associated with many PU-based methods with high-order approximations is eliminated in the present element. A number of numerical examples indicate the high accuracy and robustness of the Trig3-MLScns element. Originality/value The proposed element inherits the individual merits of the NMM and the MLS.
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Eldracher, Martin, Alexander Staller, and René Pompl. "Adaptive Encoding Strongly Improves Function Approximation with CMAC." Neural Computation 9, no. 2 (February 1, 1997): 403–17. http://dx.doi.org/10.1162/neco.1997.9.2.403.

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The Cerebellar Model Arithmetic Computer (CMAC) (Albus 1981) is well known as a good function approximator with local generalization abilities. Depending on the smoothness of the function to be approximated, the resolution as the smallest distinguishable part of the input domain plays a crucial role. If the binary quantizing functions in CMAC are dropped in favor of more general, continuous-valued functions, much better results in function approximation for smooth functions are obtained in shorter training time with less memory consumption. For functions with discontinuities, we obtain a further improvement by adapting the continuous encoding proposed in Eldracher and Geiger (1994) for difficult-to-approximate areas. Based on the already far better function approximation capability on continuous functions with a fixed topologically distributed encoding scheme in CMAC (Eldracher et al. 1994), we present the better results in learning a two-valued function with discontinuity using this adaptive topologically distributed encoding scheme in CMAC.
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HESSE, KERSTIN, and Q. T. LE GIA. "LOCAL RADIAL BASIS FUNCTION APPROXIMATION ON THE SPHERE." Bulletin of the Australian Mathematical Society 77, no. 2 (April 2008): 197–224. http://dx.doi.org/10.1017/s0004972708000087.

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AbstractIn this paper we derive local error estimates for radial basis function interpolation on the unit sphere $\mathbb {S}^2\subset \mathbb {R}^3$. More precisely, we consider radial basis function interpolation based on data on a (global or local) point set $X\subset \mathbb {S}^2$ for functions in the Sobolev space $H^s(\mathbb {S}^2)$ with norm $\|\cdot \|_s$, where s>1. The zonal positive definite continuous kernel ϕ, which defines the radial basis function, is chosen such that its native space can be identified with $H^s(\mathbb {S}^2)$. Under these assumptions we derive a local estimate for the uniform error on a spherical cap S(z;r): the radial basis function interpolant ΛXf of $f\in H^s(\mathbb {S}^2)$ satisfies $\sup _{\mathbf {x}\in S(\mathbf {z};r)} |f(\mathbf {x})-\Lambda _X f(\mathbf {x})| \leq c h^{(s-1)/2} \|f\|_{s}$, where h=hX,S(z;r) is the local mesh norm of the point set X with respect to the spherical cap S(z;r). Our proof is intrinsic to the sphere, and makes use of the Videnskii inequality. A numerical test illustrates the theoretical result.
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Singh, Satwinder Jit, and Anindya Chatterjee. "Beyond fractional derivatives: local approximation of other convolution integrals." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2114 (October 29, 2009): 563–81. http://dx.doi.org/10.1098/rspa.2009.0378.

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Dynamic systems involving convolution integrals with decaying kernels, of which fractionally damped systems form a special case, are non-local in time and hence infinite dimensional. Straightforward numerical solution of such systems up to time t needs computations owing to the repeated evaluation of integrals over intervals that grow like t . Finite-dimensional and local approximations are thus desirable. We present here an approximation method which first rewrites the evolution equation as a coupled infinite-dimensional system with no convolution, and then uses Galerkin approximation with finite elements to obtain linear, finite-dimensional, constant coefficient approximations for the convolution. This paper is a broad generalization, based on a new insight, of our prior work with fractional order derivatives ( Singh & Chatterjee 2006 Nonlinear Dyn. 45 , 183–206). In particular, the decaying kernels we can address are now generalized to the Laplace transforms of known functions; of these, the power law kernel of fractional order differentiation is a special case. The approximation can be refined easily. The local nature of the approximation allows numerical solution up to time t with computations. Examples with several different kernels show excellent performance. A key feature of our approach is that the dynamic system in which the convolution integral appears is itself approximated using another system, as distinct from numerically approximating just the solution for the given initial values; this allows non-standard uses of the approximation, e.g. in stability analyses.
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GATHERAL, JIM, and TAI-HO WANG. "THE HEAT-KERNEL MOST-LIKELY-PATH APPROXIMATION." International Journal of Theoretical and Applied Finance 15, no. 01 (February 2012): 1250001. http://dx.doi.org/10.1142/s021902491250001x.

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In this article, we derive a new most-likely-path (MLP) approximation for implied volatility in terms of local volatility, based on time-integration of the lowest order term in the heat-kernel expansion. This new approximation formula turns out to be a natural extension of the well-known formula of Berestycki, Busca and Florent. Various other MLP approximations have been suggested in the literature involving different choices of most-likely-path; our work fixes a natural definition of the most-likely-path. We confirm the improved performance of our new approximation relative to existing approximations in an explicit computation using a realistic S&P500 local volatility function.
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Generowicz, Jacek, Chris Harvey-Fros, and Tim R. Morris. "C function representation of the Local Potential Approximation." Physics Letters B 407, no. 1 (August 1997): 27–32. http://dx.doi.org/10.1016/s0370-2693(97)00729-6.

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Islam, Md Monirul, and Shyamapada Modak. "Second approximation of local functions in ideal topological spaces." Acta et Commentationes Universitatis Tartuensis de Mathematica 22, no. 2 (January 2, 2019): 245–56. http://dx.doi.org/10.12697/acutm.2018.22.20.

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This paper gives a new dimension to discuss the local function in ideal topological spaces. We calculate error operators for various type of local functions and introduce more perfect approximation of the local functions for discussing their properties. We have also reached a topological space with the help of semi-closure.
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Qasim, Mohd, M. Mursaleen, Asif Khan, and Zaheer Abbas. "Approximation by Generalized Lupaş Operators Based on q-Integers." Mathematics 8, no. 1 (January 2, 2020): 68. http://dx.doi.org/10.3390/math8010068.

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The purpose of this paper is to introduce q-analogues of generalized Lupaş operators, whose construction depends on a continuously differentiable, increasing, and unbounded function ρ . Depending on the selection of q, these operators provide more flexibility in approximation and the convergence is at least as fast as the generalized Lupaş operators, while retaining their approximation properties. For these operators, we give weighted approximations, Voronovskaja-type theorems, and quantitative estimates for the local approximation.
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Dissertations / Theses on the topic "Local approximation of a function"

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Jochym, Dominik Bogdan. "Development of non-local density functional methods." Thesis, Durham University, 2008. http://etheses.dur.ac.uk/2174/.

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Density functional theory (DFT) is a popular approach to solving the many-electron Schrödinger equation, in order to investigate the properties of matter from first principles. While DFT can give the exact ground state electronic density of a system, in practice, an approximation is required for the many-body effects contained in the exchange-correlation functional. The accuracy of calculations performed using DFT is strongly related to the choice of approximation. In this thesis we will investigate and build upon a fully non-local approach to modeling exchange-correlation in the form of the weighted density approximation (WDA). Central to the WDA is the model function chosen for the coupling-constant averaged pair-correlation function (PCF). We show that a model PCF can be selected from a set to give excellent bulk properties for a particular system. However, this model is not necessarily transferable to other systems and there is no method of selecting an appropriate model from this set a priori. We suggest that the model PCF can be improved systematically by satisfying known physical constraints. One such constraint is the Kimball cusp condition, which we include in our model and implement. We demonstrate that surfaces are systems that require a non-local treatment of exchange-correlation by applying the WDA to metal surfaces and investigate the dissociative adsorption of H2 on the Cu(100) surface. A new framework for a model PCF with spin resolution is developed, providing a route for more physical constraints to be satisfied within a weighted spin density approximation (WSDA). A simple model is suggested and implemented and comparisons are made to the coupling-constant averaged PCF in the homogeneous electron gas. We then apply a selection of our new models to a number of materials and show that our model for the WSDA gives improved band gaps over the local density approximation. Application of the WSDA to spin polarised materials reveals shortcomings in our simple model. We then suggest further refinements to our implementation of the WSDA. It is expected that the inclusion of additional physical constraints will systematically improve results given in a weighted-density based approximation to exchange-correlation.
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Générau, François. "Sur une approximation variationnelle stable du cut locus, et un problème isopérimetrique non local." Thesis, Université Grenoble Alpes, 2020. http://www.theses.fr/2020GRALM014.

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Cette thèse comporte deux parties. Dans la première partie, nous étudions une généralisation du problème variationnel de torsion élastique-plastique à des variétés. Nous montrons que dans le cas des variétés, le problème n'est pas équivalent à un problème d'obstacle, contrairement au cas euclidien, mais nous établissons l'équivalence lorsque le paramètre du problème tend vers l'infini. Nous montrons, comme dans le cas euclidien, que l'ensemble de non contact contient le cut locus de la variété, et converge vers ce dernier au sens de Hausforff. Nous montrons de plus que les miniseurs du problème sont uniformément semiconcaves. Nous en déduisons une approximation stable de cut locus, dans l'esprit du lambda axe médian de Chazal et Lieutier. Nous utilisons ensuite ce résultat pour calculer numériquement le cut locus de surfaces de géométries variées.Dans la seconde partie, nous étudions une extension d'un problème isopérimétrique non local. Précisément, on adjoint un potentiel de confinement au modèle de goutte liquide du noyau de Gamow. Nous étudions alors les minimiseurs de grand volume. Nous montrons que pour certains jeux de paramètres, les minimiseurs de grand volume convergent vers des boules, voire sont exactement des boules. Nous développons ensuite une méthode numérique pour ce problème variationnel. Cela permet de confirmer numériquement une conjecture de Choksi et Peletier en dimension 2 : dans ce cas les minimiseurs du modèle de Gamow semble être des boules si ils existent
This thesis is composed of two parts. In the first part, we study a generalization of the variational problem of elastic-plastic torsion problem to manifolds. We show that in the case of manifolds, the problem is not equivalent to an obstacle type problem, contrary to the euclidean case, but we establish the equivalence when the parameter of the problem goes to infinity. We show, as in the euclidean case, that the non contact set contains the cut locus of the manifold, and converges to the latter in the Hausdorff sense. What is more, we show that the minimizers of the problem are uniformly semiconcave. We deduce a stable approximation of the cut locus, in the spirit of the lambda medial axis of Chazal and Lieutier. We then use this result to compute numerically the cut locus of some surfaces of varied geometries.In the second part, we study an extension of a nonlocal isoperimetric problem. More precisely, we add a confinement potential to Gamow's liquid drop model for the nucleus. We then study large volume minimizers. We show that for certain sets of parameters, large volume minimizers converge to the ball, or may even exactly be the ball. Moreover, we develop a numerical method for this variational problem. Our results confirm numerically a conjecture of Choksi and Peletier, in dimension 2: it seems that minimizers of Gamow'sliquid drop model are balls as long as they exist
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Yasuda, Koji. "Local Approximation of the Correlation Energy Functional in the Density Matrix Functional Theory." American Physical Society, 2002. http://hdl.handle.net/2237/8743.

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Mancini, Lorenzo. "Adiabatic and local approximations for the kohn-sham potential in the hubbard model." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2013. http://amslaurea.unibo.it/5935/.

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We obtain the exact time-dependent Kohn-Sham potentials Vks for 1D Hubbard chains, driven by a d.c. external field, using the time-dependent electron density and current density obtained from exact many-body time-evolution. The exact Vxc is compared to the adiabatically-exact Vad-xc and the “instantaneous ground state” Vigs-xc. The effectiveness of these two approximations is analyzed. Approximations for the exchange-correlation potential Vxc and its gradient, based on the local density and on the local current density, are also considered and both physical quantities are observed to be far outside the reach of any possible local approximation. Insight into the respective roles of ground-state and excited-state correlation in the time-dependent system, as reflected in the potentials, is provided by the pair correlation function.
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Izquierdo, Diego. "Dualité et principe local-global sur les corps de fonctions." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS345/document.

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Dans cette thèse, nous nous intéressons à l'arithmétique de certains corps de fonctions. Nous cherchons à établir dans un premier temps des théorèmes de dualité arithmétique sur ces corps, pour les appliquer ensuite à l'étude des points rationnels sur certaines variétés algébriques. Dans les trois premiers chapitres, nous travaillons sur le corps des fonctions d'une courbe sur un corps local supérieur (comme Qp, Qp((t)), C((t)) ou C((t))((u))). Dans le premier chapitre, nous établissons sur un tel corps des théorèmes de dualité arithmétique « à la Poitou-Tate » pour les modules finis, les tores, et même pour certains complexes de tores. Nous montrons aussi l'existence, sous certaines hypothèses, de certaines portions des suites exactes de Poitou-Tate correspondantes. Ces résultats sont appliqués dans le deuxième chapitre à l'étude du principe local-global pour les algèbres simples centrales, de l'approximation faible pour les tores, et des obstructions au principe local-global pour les torseurs sous des groupes linéaires connexes. Dans le troisième chapitre, nous nous penchons sur les variétés abéliennes et établissons des théorèmes de dualité arithmétique « à la Cassels-Tate ». Cela demande aussi de mener une étude fine des variétés abéliennes sur les corps locaux supérieurs. Dans le quatrième et dernier chapitre, nous travaillons sur les corps des fractions de certaines algèbres locales normales de dimension 2 (typiquement C((x, y)) ou Fp((x, y))). Nous établissons d'abord un théorème de dualité en cohomologie étale « à la Artin-Verdier » dans ce contexte. Cela nous permet ensuite de montrer des théorèmes de dualité arithmétique en cohomologie galoisienne « à la Poitou-Tate » pour les modules finis et les tores. Nous appliquons finalement ces résultats à l'étude de l'approximation faible pour les tores et des obstructions au principe local-global pour les torseurs sous des groupes linéaires connexes
In this thesis, we are interested in the arithmetic of some function fields. We first want to establish arithmetic duality theorems over those fields, in order to apply them afterwards to the study of rational points on algebraic varieties. In the first three chapters, we work on the function field of a curve defined over a higher-dimensional local field (such as Qp, Qp((t)), C((t)) or C((t))((u))). In the first chapter, we establish "Poitou-Tate type" arithmetic duality theorems over such fields for finite modules, tori and even some complexes of tori. We also prove the existence, under some hypothesis, of parts of the corresponding Poitou-Tate exact sequences. These results are applied in the second chapter to the study of the local-global principle for central simple algebras, of weak approximation for tori, and of obstructions to local-global principle for torsors under connected linear algebraic groups. In the third chapter, we are interested in abelian varieties and we establish "Cassels-Tate type" arithmetic duality theorems. To do so, we also need to carry out a precise study of abelian varieties over higher-dimensional local fields. In the fourth and last chapter, we work on the field of fractions of some 2-dimensional normal local algebras (such as C((x, y)) or Fp((x, y))). We first establish in this context an "Artin-Verdier type" duality theorem in étale cohomology. This allows us to prove "Poitou-Tate type" arithmetic duality theorems in Galois cohomology for finite modules and tori. In the end, we apply these results to the study of weak approximation for tori and of obstructions to local-global principle for torsors under connected linear algebraic groups
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Belhaj, Amor Fatma. "Enseignement et apprentissage des approximations locales des fonctions au début du cursus dans le Supérieur - Cas des classes préparatoires aux études d'ingénieurs." Electronic Thesis or Diss., Pau, 2022. https://theses.hal.science/tel-04051033.

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Au début du cycle des classes préparatoires aux études d'ingénieurs, les concepts de la relation de comparaison des fonctions, la formule de Taylor-Young et développements limités ont pour caractéristique fondamentale celle de résoudre des problèmes d'approximations locales des fonctions et de modélisations physique, mécanique, optique, etc. Une revue de lecture des travaux liés au domaine de didactique de l'Analyse nous a conduit à émettre l'hypothèse que l'identification et la caractérisation des obstacles liés à l'appropriation et à l'usage raisonné des notions d'approximation locale d'une fonction, contribuent significativement à étudier la nature et l'origine des difficultés rencontrées par les étudiants concernant la conceptualisation de ces objets en première année de section Physique-Chimie (PC). Ces obstacles résultent a priori en grande partie de l'absence des situations mathématiques dévolues aux étudiants nécessitant l'utilisation des représentations graphiques. Afin de surmonter ces obstacles de natures épistémologique, didactique et culturelle et de permettre aux étudiants de donner du sens au concept d'approximation locale d'une fonction, nous avons élaboré et mis en œuvre, en collaboration avec l'enseignante de la classe de première année (PC), une ingénierie didactique de développement par l'intégration de deux situations à dimension adidactique dans l'enseignement du chapitre « Analyse asymptotique ». Cette ingénierie, construite dans le cadre de la théorie des situations didactiques, vise à introduire ce concept par l'articulation des dimensions sémantique et syntaxique et la mobilisation de ses différentes représentations en utilisant un logiciel dynamique de géométrie Geogebra pour des constructions graphiques. L'analyse didactique des raisonnements, qui sous-tendent les procédures de résolution des étudiants, nous renseigne très précisément sur les connaissances et les savoirs mobilisés par confrontation aux différentes situations, sur la nature et le type de raisonnements ainsi que sur les dimensions sémantique et/ou syntaxique inhérentes à ses différentes étapes. Dans notre travail, l'expérimentation combinant la visualisation des représentations graphiques « dynamiques » et les raisonnements mathématiques, produits par les étudiants par la mobilisation de leurs connaissances antérieures sur l'étude d'une fonction, ont contribué à une approche analytique permettant l'introduction de la définition formelle du développement limité avec toute la complexité du travail dans le paradigme [Analyse Infinitésimale] qui couple la topologie et l'Analyse fonctionnelle. L'ingénierie a également permis, au sein des groupes et en classe entière, de générer des discussions, d'amener des échanges et de faire percevoir aux étudiants la richesse de l'articulation des différentes représentations du concept d'approximation locale d'une fonction pour poser des raisonnements articulant les dimensions sémantique et syntaxique. De ce fait, au lieu de se concentrer initialement sur le processus formel de la conceptualisation du développement limité d'ordre n d'une fonction au voisinage d'un réel, il devient possible de cibler précisément les représentations graphiques d'une fonction et de ses approximations polynômiales successives (d'ordre 1, 2, 3 et 4) en tant qu'objet pour visualiser l'amélioration de l'approximation polynômiale lorsque l'ordre augmente ; ainsi l'erreur d'approximation diminue et elle sera « meilleure » au voisinage de ce réel. L'ingénierie a permis l'adaptation des situations produites aux conditions ordinaires d'enseignement et aux besoins des enseignants. Cette étude pourra ainsi jouer un rôle dans la formation des enseignants du point de vue de la construction des connaissances, de l'importance de contrat didactique et de l'ouverture sur leur formation par l'usage du cadre graphique par un travail dans l'environnement de la technologie lors de l'enseignement des nouvelles notions au niveau Supérieur
At the beginning of the preparatory classes for engineering studies, the concepts of the comparison relation of functions, the Taylor-Young formula and limited developments have as a fundamental characteristic that of solving problems of local approximations of functions and of physical, mechanical, optical modelling, etc. A review of works related to the didactical field of Analysis led us to the hypothesis that the identification and the characterization of the obstacles related to the appropriation and the reasoned use of the notions of local approximation of a function, contribute significantly to the study of the nature and the origin of the difficulties encountered by the students concerning the conceptualization of these objects in the first year of the Physics-Chemistry section (PC). These obstacles result a priori in large part from the absence of mathematical situations devolved to the students requiring the use of graphical representations. In order to overcome these epistemological, didactical and cultural obstacles and to allow the students to give meaning to the concept of local approximation of a function, we have elaborated and implemented, in collaboration with the teacher of the first year class (PC), a didactical engineering of development by the integration of two situations with an adidactical dimension in the teaching of the chapter "Asymptotic analysis". This engineering, built within the framework of the theory of didactical situations, aims at introducing this concept by the articulation of the semantic and syntactic dimensions and the mobilization of its various representations by using a dynamic software of geometry Geogebra for graphic constructions. The didactical analysis of the reasoning, which underlie the resolution procedures of the students, informs us very precisely on the knowledge and the knowledges mobilized by confrontation with the various situations, on the nature and the type of reasonings as well as on the semantic and/or syntactic dimensions inherent to its various stages. In our work, the experimentation combining the visualization of "dynamic" graphical representations and the mathematical reasoning, produced by the students by mobilizing their previous knowledge on the study of a function, contributed to an analytical approach allowing the introduction of the formal definition of the limited development with all the complexity of the work in the paradigm [Infinitesimal Analysis] which couples topology and Functional Analysis. Engineering also allowed, within the groups and in the whole class, to generate discussions, to bring exchanges and to make the students perceive the richness of the articulation of the various representations of the concept of local approximation of a function to pose reasoning articulating the semantic and syntactic dimensions. Thus, instead of focusing initially on the formal process of conceptualizing the limited development of order n of a function in the neighborhood of a real, it becomes possible to precisely target the graphical representations of a function and its successive polynomial approximations (of order 1, 2, 3 and 4) as an object to visualize the improvement of the polynomial approximation when the order increases; thus the approximation error decreases and it will be "better" in the neighborhood of this real. The engineering allowed the adaptation of the situations produced to the ordinary conditions of teaching and to the needs of the teachers. This study will thus be able to play a role in the training of teachers from the point of view of the construction of knowledge, the importance of didactical contract and the opening on their training by the use of the graphic framework by a work in the environment of technology at the time of the teaching of the new concepts at the Higher level
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Phan, Anh cang. "Crack removal and hole filling on composite subdivision meshes." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4068/document.

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Construire une surface lisse d'un objet 3D est un problème important dans de nombreuses applications graphiques. En particulier, les méthodes de subdivision permettent de passer facilement d'un maillage discret à une surface continue. Un problème général résultant de la subdivision de deux maillages initialement connectés le long d'un bord est l'apparition de fissures ou de trous entre eux. Ces fissures produisent non seulement des formes indésirables, mais induisent aussi des difficultés pour les traitements ultérieurs. Il faut donc réparer ces défauts de sorte que la surface obtenue soit lisse et puisse être subdivisée ou modifiée. Nous proposons de nouvelles méthodes pour relier deux maillages avec des résolutions différentes en utilisant une transformée en ondelettes B-splines et une approximation locale ou une interpolation locale à l'aide de fonctions de base radiales (RBF). Ces procédés génèrent un maillage de connexion où la continuité est contrôlée. La résolution du maillage est ajustable pour respecter le changement de résolution entre les zones grossières et fines. En outre, nous présentons des méthodes pour combler les trous à n-côtés, et le raffinement des maillages grâce à un schéma de subdivision adaptative. Nous avons conçu, implémenté et testé les algorithmes en MatLab pour illustrer nos méthodes et montrer des résultats expérimentaux. Ces algorithmes sont mis en oeuvre sur de nombreux modèles d'objets 3D avec des formes complexes. En outre, nous avons fourni des approches différentes pour chaque problème. Ainsi, les résultats des différentes approches sont comparés et évalués afin d'exploiter les avantages et les inconvénients de ces approches
Constructing a smooth surface of a 3D object is an important problem in many graphical applications. In particular, subdivision methods permit to pass easily from a discrete mesh to a continuous surface. A generic problem arising from subdividing two meshes initially connected along a common boundary is the occurrence of cracks or holes between them. These cracks not only produce undesired shapes, but also bring serious trouble for further mesh processing. They must be removed or filled so that the produced surface is smooth and can be further subdivided or edited. In order to remove cracks, we propose new methods for joining two meshes with different resolutions using a Lifted B-spline wavelet transform and a local approximation or radial basis function (RBF) local interpolation. These methods generate a connecting mesh where continuity is controlled from one boundary to the other and the connecting mesh can change gradually in resolution between coarse and fine areas. Additionally, we introduce methods for filling n-sided holes, and refining meshes with an adaptive subdivision scheme. We have designed, implemented, and tested the algorithms in MatLab to illustrate our proposed methods and show experimental results. These algorithms are implemented on many 3D object models with complex shapes. Additionally, we have provided some different approaches for each problem. Thus, results from the different approaches are compared and evaluated to exploit the advantages and disadvantages of these approaches
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Tas, Murat. "Dielectric Formulation Of The One Dimensional Electron Gas." Phd thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12604981/index.pdf.

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The charge and spin density correlations in a one dimensional electron gas (1DEG) confined in a semiconductor quantum wire structure at zero temperature are studied. The dielectric formulation of the many--body problem is employed and the longitudinal dielectric function, local-field correction, static structure factor, pair correlation function, ground state energy, compressibility, spin-dependent effective interaction potentials, paramagnon dispersion and static spin response function of the 1DEG are computed within the self-consistent field approximations of Singwi et al., known as the STLS and SSTL. The results are compared with those of other groups, and those obtained for two-dimensional electron gas systems whenever it is possible. It is observed that the SSTL satisfies the compressibility sum rule better than the STLS. Calculating the ground state energy of the 1DEG in unpolarized and fully polarized states, it is shown that both STLS and SSTL predict a Bloch transition for 1DEG systems at low electron densities. Finally, the coupled plasmon-phonon modes in semiconductor quantum wires are calculated within the Fermi and Luttinger liquid theories. The coupling of electrons to bulk longitudinal optical phonons without dispersion and to acoustic phonons via deformation potential with a linear dispersion are considered. Using the dielectric formalism, a unified picture of the collective coupled plasmon-phonon modes is presented. Considerable differences between the predictions of the Fermi and Luttinger liquid approaches at large wave vector values, which may be observed experimentally, are found.
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De, Silva Shalutha. "Force controlled hexapod walking." Thesis, Queensland University of Technology, 2014. https://eprints.qut.edu.au/78978/1/Karunakalage_De%20Silva_Thesis.pdf.

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This thesis is a study on controlling methods for six-legged robots. The study is based on mathematical modeling and simulation. A new joint controller is proposed and tested in simulation that uses joint angles and leg reaction force as inputs to generate a torque, and a method to optimise this controller is formulated and validated. Simulation shows that hexapod can walk on flat ground based on PID controllers with just four target configurations and a set of leg coordination rules, which provided the basis for the design of the new controller.
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Madani, Soffana. "Contributions à l’estimation à noyau de fonctionnelles de la fonction de répartition avec applications en sciences économiques et de gestion." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1183/document.

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La répartition des revenus d'une population, la distribution des instants de défaillance d'un matériel et l'évolution des bénéfices des contrats d'assurance vie - étudiées en sciences économiques et de gestion – sont liées a des fonctions continues appartenant à la classe des fonctionnelles de la fonction de répartition. Notre thèse porte sur l'estimation à noyau de fonctionnelles de la fonction de répartition avec applications en sciences économiques et de gestion. Dans le premier chapitre, nous proposons des estimateurs polynomiaux locaux dans le cadre i.i.d. de deux fonctionnelles de la fonction de répartition, notées LF et TF , utiles pour produire des estimateurs lisses de la courbe de Lorenz et du temps total de test normalisé (scaled total time on test transform). La méthode d'estimation est décrite dans Abdous, Berlinet et Hengartner (2003) et nous prouvons le bon comportement asymptotique des estimateurs polynomiaux locaux. Jusqu'alors, Gastwirth (1972) et Barlow et Campo (1975) avaient défini des estimateurs continus par morceaux de la courbe de Lorenz et du temps total de test normalisé, ce qui ne respectait pas la propriété de continuité des courbes initiales. Des illustrations sur données simulées et réelles sont proposées. Le second chapitre a pour but de fournir des estimateurs polynomiaux locaux dans le cadre i.i.d. des dérivées successives des fonctionnelles de la fonction de répartition explorées dans le chapitre précédent. A part l'estimation de la dérivée première de la fonction TF qui se traite à l'aide de l'estimation lisse de la fonction de répartition, la méthode d'estimation employée est l'approximation polynomiale locale des fonctionnelles de la fonction de répartition détaillée dans Berlinet et Thomas-Agnan (2004). Divers types de convergence ainsi que la normalité asymptotique sont obtenus, y compris pour la densité et ses dérivées successives. Des simulations apparaissent et sont commentées. Le point de départ du troisième chapitre est l'estimateur de Parzen-Rosenblatt (Rosenblatt (1956), Parzen (1964)) de la densité. Nous améliorons dans un premier temps le biais de l'estimateur de Parzen-Rosenblatt et de ses dérivées successives à l'aide de noyaux d'ordre supérieur (Berlinet (1993)). Nous démontrons ensuite les nouvelles conditions de normalité asymptotique de ces estimateurs. Enfin, nous construisons une méthode de correction des effets de bord pour les estimateurs des dérivées de la densité, grâce aux dérivées d'ordre supérieur. Le dernier chapitre s'intéresse au taux de hasard, qui contrairement aux deux fonctionnelles de la fonction de répartition traitées dans le premier chapitre, n'est pas un rapport de deux fonctionnelles linéaires de la fonction de répartition. Dans le cadre i.i.d., les estimateurs à noyau du taux de hasard et de ses dérivées successives sont construits à partir des estimateurs à noyau de la densité et ses dérivées successives. La normalité asymptotique des premiers estimateurs est logiquement obtenue à partir de celle des seconds. Nous nous plaçons ensuite dans le modèle à intensité multiplicative, un cadre plus général englobant des données censurées et dépendantes. Nous menons la procédure à terme de Ramlau-Hansen (1983) afin d'obtenir les bonnes propriétés asymptotiques des estimateurs du taux de hasard et de ses dérivées successives puis nous tentons d'appliquer l'approximation polynomiale locale dans ce contexte. Le taux d'accumulation du surplus dans le domaine de la participation aux bénéfices pourra alors être estimé non parametriquement puisqu'il dépend des taux de transition (taux de hasard d'un état vers un autre) d'une chaine de Markov (Ramlau-Hansen (1991), Norberg (1999))
The income distribution of a population, the distribution of failure times of a system and the evolution of the surplus in with-profit policies - studied in economics and management - are related to continuous functions belonging to the class of functionals of the distribution function. Our thesis covers the kernel estimation of some functionals of the distribution function with applications in economics and management. In the first chapter, we offer local polynomial estimators in the i.i.d. case of two functionals of the distribution function, written LF and TF , which are useful to produce the smooth estimators of the Lorenz curve and the scaled total time on test transform. The estimation method is described in Abdous, Berlinet and Hengartner (2003) and we prove the good asymptotic behavior of the local polynomial estimators. Until now, Gastwirth (1972) and Barlow and Campo (1975) have defined continuous piecewise estimators of the Lorenz curve and the scaled total time on test transform, which do not respect the continuity of the original curves. Illustrations on simulated and real data are given. The second chapter is intended to provide smooth estimators in the i.i.d. case of the derivatives of the two functionals of the distribution function presented in the last chapter. Apart from the estimation of the first derivative of the function TF with a smooth estimation of the distribution function, the estimation method is the local polynomial approximation of functionals of the distribution function detailed in Berlinet and Thomas-Agnan (2004). Various types of convergence and asymptotic normality are obtained, including the probability density function and its derivatives. Simulations appear and are discussed. The starting point of the third chapter is the Parzen-Rosenblatt estimator (Rosenblatt (1956), Parzen (1964)) of the probability density function. We first improve the bias of this estimator and its derivatives by using higher order kernels (Berlinet (1993)). Then we find the modified conditions for the asymptotic normality of these estimators. Finally, we build a method to remove boundary effects of the estimators of the probability density function and its derivatives, thanks to higher order derivatives. We are interested, in this final chapter, in the hazard rate function which, unlike the two functionals of the distribution function explored in the first chapter, is not a fraction of two linear functionals of the distribution function. In the i.i.d. case, kernel estimators of the hazard rate and its derivatives are produced from the kernel estimators of the probability density function and its derivatives. The asymptotic normality of the first estimators is logically obtained from the second ones. Then, we are placed in the multiplicative intensity model, a more general framework including censored and dependent data. We complete the described method in Ramlau-Hansen (1983) to obtain good asymptotic properties of the estimators of the hazard rate and its derivatives and we try to adopt the local polynomial approximation in this context. The surplus rate in with-profit policies will be nonparametrically estimated as its mathematical expression depends on transition rates (hazard rates from one state to another) in a Markov chain (Ramlau-Hansen (1991), Norberg (1999))
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Books on the topic "Local approximation of a function"

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I, Anisimov V., ed. Strong coulomb correlations in electronic structure calculations: Beyond the local density approximation. Amsterdam, The Netherlands: Gordon and Breach Science Publishers, 2000.

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1934-, Ciesielski Zbigniew, ed. Approximation and function spaces. Warszawa: PWN-Polish Scientific Publishers, 1989.

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Lewis Research Center. Institute for Computational Mechanics in Propulsion., ed. On the convergence of local approximations to pseudodifferential operators with applications. Cleveland, Ohio: Institute for Computational Mechanics in Propulsion, Lewis Research Center, 1994.

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Katkovnik, V. I︠A︡. Local approximation techniques in signal and image processing. Bellingham, Wash: SPIE Press, 2006.

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Steve, Leach, ed. Local government: It's role and function. York: Joseph Rowntree Foundation, 1992.

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Nikolʹskiĭ, S. M. Izbrannye trudy: V trekh tomakh. Moskva: Nauka, 2006.

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Domich, P. D. A near-optimal starting solution for polynomial approximation of a continuous function in the L. [Washington, D.C.]: U.S. Dept. of Commerce, National Bureau of Standards, 1986.

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Domich, P. D. A near-optimal starting solution for polynomial approximation of a continuous function in the L. [Washington, D.C.]: U.S. Dept. of Commerce, National Bureau of Standards, 1986.

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Hedberg, Lars Inge. An axiomatic approach to function spaces, spectral synthesis, and Luzin approximation. Providence, RI: American Mathematical Society, 2007.

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Domich, P. D. A near-optimal starting solution for polynomial approximation of a continuous function in the Lb1s norm. [Washington, D.C.]: U.S. Dept. of Commerce, National Bureau of Standards, 1986.

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Book chapters on the topic "Local approximation of a function"

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Jonsson, Alf. "Markov’s inequality and local polynomial approximation." In Function Spaces and Applications, 303–16. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0078881.

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Korostelev, Alexander, and Olga Korosteleva. "Local polynomial approximation of regression function." In Graduate Studies in Mathematics, 115–30. Providence, Rhode Island: American Mathematical Society, 2011. http://dx.doi.org/10.1090/gsm/119/09.

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Kim, Bo-Hyun, Daewon Lee, and Jaewook Lee. "Local Volatility Function Approximation Using Reconstructed Radial Basis Function Networks." In Advances in Neural Networks - ISNN 2006, 524–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11760191_77.

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Mhaskar, H. N. "Local Approximation Using Hermite Functions." In Springer Optimization and Its Applications, 341–62. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49242-1_16.

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Soós, Anna, and Ildikó Somogyi. "Approximation Method with Stochastic Local Iterated Function Systems." In Lecture Notes in Computational Science and Engineering, 881–89. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-55874-1_87.

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Liu, Jinkun. "Adaptive Robust RBF Control Based on Local Approximation." In Radial Basis Function (RBF) Neural Network Control for Mechanical Systems, 193–249. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34816-7_7.

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Pluciński, Marcin. "Mini-models – Local Regression Models for the Function Approximation Learning." In Artificial Intelligence and Soft Computing, 160–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29350-4_19.

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Vamplew, Peter, and Robert Ollington. "Global Versus Local Constructive Function Approximation for On-Line Reinforcement Learning." In AI 2005: Advances in Artificial Intelligence, 113–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11589990_14.

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Dreizler, Reiner M., and Eberhard K. U. Gross. "Explicit Functionals II: The Local Density Approximation and Beyond." In Density Functional Theory, 173–244. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-86105-5_7.

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Engel, G. E., and Warren E. Pickett. "Density Functionals for Energies and Eigenvalues: Local Mass Approximation." In Electronic Density Functional Theory, 299–309. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4899-0316-7_21.

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Conference papers on the topic "Local approximation of a function"

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Andras, Peter. "High-dimensional function approximation using local linear embedding." In 2015 International Joint Conference on Neural Networks (IJCNN). IEEE, 2015. http://dx.doi.org/10.1109/ijcnn.2015.7280370.

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Khebbache, Selma, Makhlouf Hadji, and Djamal Zeghlache. "Dynamic Placement of Extended Service Function Chains: Steiner-based Approximation Algorithms." In 2018 IEEE 43rd Conference on Local Computer Networks (LCN). IEEE, 2018. http://dx.doi.org/10.1109/lcn.2018.8638044.

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Dolgov, Maxim, Gerhard Kurz, Daniela Grimm, Florian Rosenthal, and Uwe D. Hanebeck. "Stochastic Optimal Control using Local Sample-based Value Function Approximation." In 2018 Annual American Control Conference (ACC). IEEE, 2018. http://dx.doi.org/10.23919/acc.2018.8431584.

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Neydorf, Rudolf. "“Cut-Glue” Approximation in Problems on Static and Dynamic Mathematical Model Development." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-37236.

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The solution to the problem on building mathematical models of technical objects through the approximation of various experimental dependences is offered in the paper. This approach is especially true for modeling aircraft because the aerodynamic coefficients of their models can be obtained either by full-scale study or by computer simulation only. Currently, the experimental simulation is performed either through the regression analysis (RGA) methods, or through spline approximation. However, the RGA has a significant disadvantage, namely a poor approximability of piecewise and multiextremal dependencies. The RGA gives a rough approximation of the experimental data for similar curves. Spline approximation is free from this disadvantage. However, a high degree of discretization, a strict binding to the number of spline points, and a large number of equations, make this approach inconvenient for application when a compact model building and an analytic transformation are required. A problem solution combining the advantages of both approaches and clearing up the troubles is offered in the paper. The proposed approach is based on the regression construction of the mathematical models of the dependence fragments, the multiplicative excision of these fragments in the local functional form, and on the additive combining of these local functions into a single analytic expression. The effect is achieved by using special “selection” functions multiplicatively limiting a nonzero definition domain for each of the approximating functions. The method is named “cut-glue” by the physical analogy of the approximation techniques. The order and structure of the approximating function for each segment can be arbitrary. A significant advantage of the “cut-glue” approximation is in a single analytic expression of the whole piecewise function instead of a cumbersome system of equations. The analytical and numerical studies of the properties and operational experience of the proposed method are resulted.
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Hu, W., K. H. Saleh, and S. Azarm. "Approximation Assisted Multiobjective Optimization With Combined Global and Local Metamodeling." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-71174.

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Approximation Assisted Optimization (AAO) is widely used in engineering design problems to replace computationally intensive simulations with metamodeling. Traditional AAO approaches employ global metamodeling for exploring an entire design space. Recent research works in AAO report on using local metamodeling to focus on promising regions of the design space. However, very limited works have been reported that combine local and global metamodeling within AAO. In this paper, a new approximation assisted multiobjective optimization approach is developed. In the proposed approach, both global and local metamodels for objective and constraint functions are used. The approach starts with global metamodels for objective and constraint functions and using them it selects the most promising points from a large number of randomly generated points. These selected points are then “observed”, which means their actual objective/constraint function values are computed. Based on these values, the “best” points are grouped in multiple clustered regions in the design space and then local metamodels of objective/constraint functions are constructed in each region. All observed points are also used to iteratively update the metamodels. In this way, the predictive capabilities of the metamodels are progressively improved as the optimizer approaches the Pareto optimum frontier. An advantage of the proposed approach is that the most promising points are observed and that there is no need to verify the final solutions separately. Several numerical examples are used to compare the proposed approach with previous approaches in the literature. Additionally, the proposed approach is applied to a CFD-based engineering design example. It is found that the proposed approach is able to estimate Pareto optimum points reasonably well while significantly reducing the number of function evaluations.
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Ryu, Chungho, Joohwan Chun, and Chungyong Lee. "MFCW Radar’s Range and Velocity Estimation using Local Polynomial Approximation Based Function." In 2020 International Conference on Information and Communication Technology Convergence (ICTC). IEEE, 2020. http://dx.doi.org/10.1109/ictc49870.2020.9289208.

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Röpke, G. "Quartetting wave function approach to 20Ne: Shell model and local density approximation." In 6TH INTERNATIONAL CONFERENCE ON PRODUCTION, ENERGY AND RELIABILITY 2018: World Engineering Science & Technology Congress (ESTCON). Author(s), 2018. http://dx.doi.org/10.1063/1.5078827.

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Wang, Zhixiang, Xi Xiao, Guangwu Hu, Yao Yao, Dianyan Zhang, Zhendong Peng, Qing Li, and Shutao Xia. "Non-local Self-attention Structure for Function Approximation in Deep Reinforcement Learning." In ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2019. http://dx.doi.org/10.1109/icassp.2019.8682832.

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Chickermane, Hemant, and Hae Chang Gea. "Structural Optimization Using a Generalized Convex Approximation." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0135.

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Abstract To reduce the computational cost of structural optimization problems, a common procedure is to generate a sequence of convex, approximate subproblems and solve them in an iterative fashion. In this paper, a new local function approximation algorithm is proposed to formulate the subproblems. This new algorithm, called Generalized Convex Approximation (GCA), uses the sensitivity information of the current and previous design points to generate a sequence of convex, separable subproblems. This algorithm gives very good local approximations and leads to faster convergence for structural optimization problems. Several numerical results of structural optimization problems are presented.
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Zhang, Jinhuan, Margaret M. Wiecek, and Wei Chen. "Local Approximation of the Efficient Frontier in Robust Design." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/dac-8566.

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Abstract The multiple quality aspects of robust design have brought more and more attention in the advancement of robust design methods. Neither the Taguchi’s signal-to-noise ratio nor the weighted-sum method is adequate in addressing designer’s preference in making tradeoffs between the mean and variance attributes. An interactive multiobjective robust design procedure that follows upon the developments on relating utility function optimization to a multiobjective programming method has been proposed by the authors. This paper is an extension of our previous work on this topic. It presents a formal procedure for deriving a quadratic utility function at a candidate solution as an approximation of the efficient frontier to explore alternative robust design solutions. The proposed procedure is investigated at different locations of candidate solutions, with different ranges of interest, and for efficient frontiers with both convex and nonconvex behaviors. This quadratic utility function provides a decision maker with new information regarding how to choose a most preferred Pareto solution. As an integral part of the interactive robust design procedure, the proposed method assists designers in adjusting the preference structure and exploring alternative efficient robust design solutions. It eliminates the needs of solving the original bi-objective optimization problem repeatedly using new preference structures, which is often a computationally expensive task for problems in a complex domain. Though demonstrated for robust design problems, the principle is also applicable to any bi-objective optimization problems.
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Reports on the topic "Local approximation of a function"

1

Mattsson, Ann Elisabet, Normand Arthur Modine, Michael Paul Desjarlais, Richard Partain Muller, Mark P. Sears, and Alan Francis Wright. Beyond the local density approximation : improving density functional theory for high energy density physics applications. Office of Scientific and Technical Information (OSTI), November 2006. http://dx.doi.org/10.2172/976954.

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Cangi, Attila, Francisca Sagredo, Elizabeth Decolvenaere, and Ann E. Mattsson. Semi-local Density Functional Approximations for Bulk Surface and Confinement Physics. Office of Scientific and Technical Information (OSTI), September 2019. http://dx.doi.org/10.2172/1569522.

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Ward, Rachel A. Reliable Function Approximation and Estimation. Fort Belvoir, VA: Defense Technical Information Center, August 2016. http://dx.doi.org/10.21236/ad1013972.

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Ron, Amos. Approximation Orders of and Approximation Maps from Local Principal Shift-Invariant Spaces. Fort Belvoir, VA: Defense Technical Information Center, May 1993. http://dx.doi.org/10.21236/ada265038.

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Lin, Daw-Tung, and Judith E. Dayhoff. Network Unfolding Algorithm and Universal Spatiotemporal Function Approximation. Fort Belvoir, VA: Defense Technical Information Center, January 1994. http://dx.doi.org/10.21236/ada453011.

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Tong, C. An Adaptive Derivative-based Method for Function Approximation. Office of Scientific and Technical Information (OSTI), October 2008. http://dx.doi.org/10.2172/945874.

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Stetcu, Ionel. Investigation of fission yields in a time-dependent superfluid local density approximation. Office of Scientific and Technical Information (OSTI), February 2017. http://dx.doi.org/10.2172/1345172.

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Nagayama, Shinobu, Tsutomu Sasao, and Jon T. Butler. Programmable Numerical Function Generators Based on Quadratic Approximation: Architecture and Synthesis Method. Fort Belvoir, VA: Defense Technical Information Center, January 2006. http://dx.doi.org/10.21236/ada599939.

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Potamianos, Gerasimos, and John Goutsias. Stochastic Simulation Techniques for Partition Function Approximation of Gibbs Random Field Images. Fort Belvoir, VA: Defense Technical Information Center, June 1991. http://dx.doi.org/10.21236/ada238611.

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Longcope, Donald B. ,. Jr, Thomas Lynn Warren, and Henry Duong. Aft-body loading function for penetrators based on the spherical cavity-expansion approximation. Office of Scientific and Technical Information (OSTI), December 2009. http://dx.doi.org/10.2172/986592.

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