Relevant bibliographies by topics / APPROXIMATION OPERATORS

Academic literature on the topic 'APPROXIMATION OPERATORS'

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Published: 26 October 2023

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Journal articles on the topic "APPROXIMATION OPERATORS"

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Lyamina, O. S. "ON NORMS AND CERTAIN CHARACTERISTICS OF TRIGONOMETRIC APPROXIMATION BY BASKAKOV OPERATORS." Vestnik of Samara University. Natural Science Series 18, no. 9 (June 9, 2017): 41–51. http://dx.doi.org/10.18287/2541-7525-2012-18-9-41-51.

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The article covers actual question in the theory of approximations. It researches approximative opportunities of concrete approximating structures. In the article one of the actively studied in recent times types of approximating operators — Baskakov's trigonometric operators. Some characteristics of these operators are being investigated: norms and approximation constants, assessment and improved. In particular, the assessment of their difference is obtained.
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Duma, Adrian, and Cristian Vladimirescu. "Approximation structures and applications to evolution equations." Abstract and Applied Analysis 2003, no. 12 (2003): 685–96. http://dx.doi.org/10.1155/s1085337503301010.

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We discuss various properties of the nonlinearA-proper operators as well as a generalized Leray-Schauder principle. Also, a method of approximating arbitrary continuous operators byA-proper mappings is described. We construct, via appropriate Browder-Petryshyn approximation schemes, approximative solutions for linear evolution equations in Banach spaces.
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Tang, Weidong, Jinzhao Wu, and Dingwei Zheng. "On Fuzzy Rough Sets and Their Topological Structures." Mathematical Problems in Engineering 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/546372.

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The core concepts of rough set theory are information systems and approximation operators of approximation spaces. Approximation operators draw close links between rough set theory and topology. This paper is devoted to the discussion of fuzzy rough sets and their topological structures. Fuzzy rough approximations are further investigated. Fuzzy relations are researched by means of topology or lower and upper sets. Topological structures of fuzzy approximation spaces are given by means of pseudoconstant fuzzy relations. Fuzzy topology satisfying (CC) axiom is investigated. The fact that there exists a one-to-one correspondence between the set of all preorder fuzzy relations and the set of all fuzzy topologies satisfying (CC) axiom is proved, the concept of fuzzy approximating spaces is introduced, and decision conditions that a fuzzy topological space is a fuzzy approximating space are obtained, which illustrates that we can research fuzzy relations or fuzzy approximation spaces by means of topology and vice versa. Moreover, fuzzy pseudoclosure operators are examined.
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Anastassiou, George A. "Multivariate and abstract approximation theory for Banach space valued functions." Demonstratio Mathematica 50, no. 1 (August 28, 2017): 208–22. http://dx.doi.org/10.1515/dema-2017-0020.

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Abstract Here we study quantitatively the high degree of approximation of sequences of linear operators acting on Banach space valued Fréchet differentiable functions to the unit operator, as well as other basic approximations including those under convexity. These operators are bounded by real positive linear companion operators. The Banach spaces considered here are general and no positivity assumption is made on the initial linear operators for which we study their approximation properties. We derive pointwise and uniform estimates, which imply the approximation of these operators to the unit assuming Fréchet differentiability of functions, and then we continue with basic approximations. At the end we study the special case where the approximated function fulfills a convexity condition resulting into sharp estimates. We give applications to Bernstein operators.
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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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Yuan Wu, Pei. "Approximation by partial isometries." Proceedings of the Edinburgh Mathematical Society 29, no. 2 (June 1986): 255–61. http://dx.doi.org/10.1017/s0013091500017624.

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Let B(H) be the algebra of bounded linear operators on a complex separable Hilbert space H. The problem of operator approximation is to determine how closely each operator T ∈B(H) can be approximated in the norm by operators in a subset L of B(H). This problem is initiated by P. R. Halmo [3] when heconsidered approximating operators by the positive ones. Since then, this problem has been attacked with various classes L: the class of normal operators whose spectrum is included in a fixed nonempty closed subset of the complex plane [4], the classes of unitary operators [6] and invertible operators [1]. The purpose of this paper is to study the approximation by partial isometries.
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Zhao, Tao, and Zhenbo Wei. "On Characterization of Rough Type-2 Fuzzy Sets." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/4819353.

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Rough sets theory and fuzzy sets theory are important mathematical tools to deal with uncertainties. Rough fuzzy sets and fuzzy rough sets as generalizations of rough sets have been introduced. Type-2 fuzzy set provides additional degree of freedom, which makes it possible to directly handle high uncertainties. In this paper, the rough type-2 fuzzy set model is proposed by combining the rough set theory with the type-2 fuzzy set theory. The rough type-2 fuzzy approximation operators induced from the Pawlak approximation space are defined. The rough approximations of a type-2 fuzzy set in the generalized Pawlak approximation space are also introduced. Some basic properties of the rough type-2 fuzzy approximation operators and the generalized rough type-2 fuzzy approximation operators are discussed. The connections between special crisp binary relations and generalized rough type-2 fuzzy approximation operators are further examined. The axiomatic characterization of generalized rough type-2 fuzzy approximation operators is also presented. Finally, the attribute reduction of type-2 fuzzy information systems is investigated.
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Zayed, Mohra, Shahid Ahmad Wani, and Mohammad Younus Bhat. "Unveiling the Potential of Sheffer Polynomials: Exploring Approximation Features with Jakimovski–Leviatan Operators." Mathematics 11, no. 16 (August 21, 2023): 3604. http://dx.doi.org/10.3390/math11163604.

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In this article, we explore the construction of Jakimovski–Leviatan operators for Durrmeyer-type approximation using Sheffer polynomials. Constructing positive linear operators for Sheffer polynomials enables us to analyze their approximation properties, including weighted approximations and convergence rates. The application of approximation theory has earned significant attention from scholars globally, particularly in the fields of engineering and mathematics. The investigation of these approximation properties and their characteristics holds considerable importance in these disciplines.
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KHAN, TAQSEER, MOHD SAIF, and SHUZAAT ALI KHAN. "APPROXIMATION BY GENERALIZED q-SZASZ-MIRAKJAN ´ OPERATORS." Journal of Mathematical Analysis 12, no. 6 (December 31, 2021): 9–21. http://dx.doi.org/10.54379/jma-2021-6-2.

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In this article, we introduce generalized q−Sz´asz-Mirakjan operators and study their approximation properties. Based on the Voronovskaja’s theorem, we obtain quantitative estimates for these operators.
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Crespo, José, and Francisco Javier Montáns. "Fractional Mathematical Operators and Their Computational Approximation." Mathematical Problems in Engineering 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/4356371.

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Usual applied mathematics employs three fundamental arithmetical operators: addition, multiplication, and exponentiation. However, for example, transcendental numbers are said not to be attainable via algebraic combination with these fundamental operators. At the same time, simulation and modelling frequently have to rely on expensive numerical approximations of the exact solution. The main purpose of this article is to analyze new fractional arithmetical operators, explore some of their properties, and devise ways of computing them. These new operators may bring new possibilities, for example, in approximation theory and in obtaining closed forms of those approximations and solutions. We show some simple demonstrative examples.
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Dissertations / Theses on the topic "APPROXIMATION OPERATORS"

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Yang, Liming. "Subnormal operators, hyponormal operators, and mean polynomial approximation." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40103.

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We prove quasisimilar subdecomposable operators without eigenvalues have equal essential spectra. Therefore, quasisimilar hyponormal operators have equal essential spectra. We obtain some results on the spectral pictures of cyclic hyponormal operators. An algebra homomorphism π from H∞(G) to L(H) is a unital representation for T if π(1) = I and π(x) = T. It is shown that if the boundary of G has zero area measure, then the unital norm continuous representation for a pure hyponormal operator T is unique and is weak star continuous. It follows that every pure hyponormal contraction is in C.0 Let μ represent a positive, compactly supported Borel measure in the plane, C. For each t in [1, ∞ ), the space Pt(μ) consists of the functions in Lt(μ) that belong to the (norm) closure of the (analytic) polynomials. J. Thomson in [T] has shown that the set of bounded point evaluations, bpe μ, for Pt(μ) is a nonempty simply connected region G. We prove that the measure μ restricted to the boundary of G is absolutely continuous with respect to the harmonic measure on G and the space P2(μ)∩C(spt μ) = A(G), where C(spt μ) denotes the continuous functions on spt μ and A(G) denotes those functions continuous on G ¯ that are analytic on G. We also show that if a function f in P2(μ) is zero a.e. μ in a neighborhood of a point on the boundary, then f has to be the zero function. Using this result, we are able to prove that the essential spectrum of a cyclic, self-dual, subnormal operator is symmetric with respect to the real axis. We obtain a reduction into the structure of a cyclic, irreducible, self-dual, subnormal operator. One may assume, in this inquiry, that the corresponding P2(μ) space has bpe μ = D. Necessary and sufficient conditions for a cyclic, subnormal operator Sμ with bpe μ = D to have a self-dual are obtained under the additional assumption that the measure on the unit circle is log-integrable.
Ph. D.
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Santos, Pedro. "Approximation Methods for Convolution Operators on the Real Line." Doctoral thesis, Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200500362.

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This work is concerned with the applicability of several approximation methods (finite section method, Galerkin and collocation methods with maximum defect splines for uniform and non uniform meshes) to operators belonging to the closed subalgebra generated by operators of multiplication bz piecewise continuous functions and convolution operators also with piecewise continuous generating function.
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Silva, Nunes Ana Luisa. "Spectral approximation with matrices issued from discretized operators." Phd thesis, Université Jean Monnet - Saint-Etienne, 2012. http://tel.archives-ouvertes.fr/tel-00952977.

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In this thesis, we consider the numerical solution of a large eigenvalue problem in which the integral operator comes from a radiative transfer problem. It is considered the use of hierarchical matrices, an efficient data-sparse representation of matrices, especially useful for large dimensional problems. It consists on low-rank subblocks leading to low memory requirements as well as cheap computational costs. We discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and hence it is weakly singular. We access HLIB (Hierarchical matrices LIBrary) that provides, among others, routines for the construction of hierarchical matrix structures and arithmetic algorithms to perform approximative matrix operations. Moreover, it is incorporated the matrix-vector multiply routines from HLIB, as well as LU factorization for preconditioning, into SLEPc (Scalable Library for Eigenvalue Problem Computations) in order to exploit the available algorithms to solve eigenvalue problems. It is also developed analytical expressions for the approximate degenerate kernels and deducted error upper bounds for these approximations. The numerical results obtained with other approaches to solve the problem are used to compare with the ones obtained with this technique, illustrating the efficiency of the techniques developed and implemented in this work
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Qiu, James Zhijan. "Polynomial approximation and Carleson measures on a general domain and equivalence classes of subnormal operators." Diss., This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-06062008-171825/.

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Saad, Nasser. "Geometrical approximation methods for the discrete spectra of Schröedinger operators." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0017/NQ44809.pdf.

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Hansen, A. C. "On the approximation of spectra of linear Hilbert space operators." Thesis, University of Cambridge, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603665.

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The main topic of this thesis is how to approximate and compute spectra of linear operators on separable Hilbert spaces. We consider several approaches including the finite section method, an infinite-dimensional version of the QR algorithm, as well as pseudospectral techniques. Several new theorems about convergence of the finite section method (and variants of it) for self-adjoint problems are obtained together with a rigorous analysis of the infinite-dimensional QR algorithm for normal operators. To attack the general spectral problem we look to the pseudospectral theory and introduce the complexity index. A generalization of the pseudospectrum is introduced, namely, the n-pseudospectrum. This set behaves very much like the original pseudospectrum, but has the advantage that it approximates the spectrum well for large n. The complexity index is a tool for indicating how complex or difficult it may be to approximate spectra of operators belonging to a certain class. We establish bounds on the complexity indeed and discuss some open problems regarding this new mathematical entity. As the approximation framework also gives rise to several computational methods, we analyze and discuss implementation techniques for algorithms that can be derived from the theoretical model. In particular, we develop algorithms that can compute spectra of arbitrary bounded operators on separable Hilbert spaces, and the exposition is followed by several numerical examples. The thesis also contains a thorough discussion on how to implement the QR algorithm in infinite dimensions. This is supported by numerical computations. These examples reveal several surprisingly nice features of the infinite-dimensional QR algorithm, and this leaves a number of open problems that we debate.
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Feijoo, Juan Alejandro Vazquez. "Analysis and identification of nonlinear system using parametric models of Volterra operators." Thesis, University of Sheffield, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.274962.

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Lindner, Marko. "Fredholm Theory and Stable Approximation of Band Operators and Their Generalisations." Doctoral thesis, Universitätsbibliothek Chemnitz, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200901182.

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This text is concerned with the Fredholm theory and stable approximation of bounded linear operators generated by a class of infinite matrices $(a_{ij})$ that are either banded or have certain decay properties as one goes away from the main diagonal. The operators are studied on $\ell^p$ spaces of functions $\Z^N\to X$, where $p\in[1,\infty]$, $N\in\N$ and $X$ is a complex Banach space. The latter means that our matrix entries $a_{ij}$ are indexed by multiindices $i,j\in\Z^N$ and that every $a_{ij}$ is itself a bounded linear operator on $X$. Our main focus lies on the case $p=\infty$, where new results are derived, and it is demonstrated in both general theory and concrete operator equations from mathematical physics how advantage can be taken of these new $p=\infty$ results in the general case $p\in[1,\infty]$.
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Borovyk, Vita. "Box approximation and related techniques in spectral theory." Diss., Columbia, Mo. : University of Missouri-Columbia, 2008. http://hdl.handle.net/10355/5566.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2008.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 2, 2009) Vita. Includes bibliographical references.
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Salim, Adil. "Random monotone operators and application to stochastic optimization." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLT021/document.

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Cette thèse porte essentiellement sur l'étude d'algorithmes d'optimisation. Les problèmes de programmation intervenant en apprentissage automatique ou en traitement du signal sont dans beaucoup de cas composites, c'est-à-dire qu'ils sont contraints ou régularisés par des termes non lisses. Les méthodes proximales sont une classe d'algorithmes très efficaces pour résoudre de tels problèmes. Cependant, dans les applications modernes de sciences des données, les fonctions à minimiser se représentent souvent comme une espérance mathématique, difficile ou impossible à évaluer. C'est le cas dans les problèmes d'apprentissage en ligne, dans les problèmes mettant en jeu un grand nombre de données ou dans les problèmes de calcul distribué. Pour résoudre ceux-ci, nous étudions dans cette thèse des méthodes proximales stochastiques, qui adaptent les algorithmes proximaux aux cas de fonctions écrites comme une espérance. Les méthodes proximales stochastiques sont d'abord étudiées à pas constant, en utilisant des techniques d'approximation stochastique. Plus précisément, la méthode de l'Equation Differentielle Ordinaire est adaptée au cas d'inclusions differentielles. Afin d'établir le comportement asymptotique des algorithmes, la stabilité des suites d'itérés (vues comme des chaines de Markov) est étudiée. Ensuite, des généralisations de l'algorithme du gradient proximal stochastique à pas décroissant sont mises au point pour resoudre des problèmes composites. Toutes les grandeurs qui permettent de décrire les problèmes à résoudre s'écrivent comme une espérance. Cela inclut un algorithme primal dual pour des problèmes régularisés et linéairement contraints ainsi qu'un algorithme d'optimisation sur les grands graphes
This thesis mainly studies optimization algorithms. Programming problems arising in signal processing and machine learning are composite in many cases, i.e they exhibit constraints and non smooth regularization terms. Proximal methods are known to be efficient to solve such problems. However, in modern applications of data sciences, functions to be minimized are often represented as statistical expectations, whose evaluation is intractable. This cover the case of online learning, big data problems and distributed computation problems. To solve this problems, we study in this thesis proximal stochastic methods, that generalize proximal algorithms to the case of cost functions written as expectations. Stochastic proximal methods are first studied with a constant step size, using stochastic approximation techniques. More precisely, the Ordinary Differential Equation method is adapted to the case of differential inclusions. In order to study the asymptotic behavior of the algorithms, the stability of the sequences of iterates (seen as Markov chains) is studied. Then, generalizations of the stochastic proximal gradient algorithm with decreasing step sizes are designed to solve composite problems. Every quantities used to define the optimization problem are written as expectations. This include a primal dual algorithm to solve regularized and linearly constrained problems and an optimization over large graphs algorithm
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Books on the topic "APPROXIMATION OPERATORS"

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Linear operator equations: Approximation and regularization. New Jersey: World Scientific, 2009.

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Approximation of Hilbert space operators. 2nd ed. Harlow, Essex, England: Longman Scientific & Technical, 1989.

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Chaitin-Chatelin, Françoise. Spectral approximation of linear operators. Philadelphia: Society for Industrial and Applied Mathematics, 2011.

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Bede, Barnabás, Lucian Coroianu, and Sorin G. Gal. Approximation by Max-Product Type Operators. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-34189-7.

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Păltănea, Radu. Approximation Theory Using Positive Linear Operators. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-2058-9.

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Cepedello Boiso, Manuel, Håkan Hedenmalm, Marinus A. Kaashoek, Alfonso Montes Rodríguez, and Sergei Treil, eds. Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0648-0.

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Gupta, Vijay, and Michael Th Rassias. Moments of Linear Positive Operators and Approximation. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-19455-0.

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Carl, Bernd. Entropy, compactness, and the approximation of operators. Cambridge: Cambridge University Press, 1990.

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Markov operators, positive semigroups, and approximation processes. Berlin: Walter de Gruyter GmbH & Co., KG, 2015.

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Anastassiou, George A. Frontiers in approximation theory. New Jersey: World Scientific, 2015.

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Book chapters on the topic "APPROXIMATION OPERATORS"

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de Villiers, Johan. "Approximation Operators." In Mathematics of Approximation, 85–98. Paris: Atlantis Press, 2012. http://dx.doi.org/10.2991/978-94-91216-50-3_5.

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DeVore, Ronald A., and George G. Lorentz. "Approximation by Operators." In Grundlehren der mathematischen Wissenschaften, 267–302. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-02888-9_9.

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Anastassiou, George A., and Sorin G. Gal. "Shift Invariant Univariate Integral Operators." In Approximation Theory, 279–95. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1360-4_10.

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Anastassiou, George A., and Sorin G. Gal. "Shift Invariant Multivariate Integral Operators." In Approximation Theory, 297–323. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1360-4_11.

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Maz’ya, Vladimir, and Gunther Schmidt. "Approximation of integral operators." In Approximate Approximations, 69–91. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/141/04.

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Anastassiou, George A., and Sorin G. Gal. "Differentiated Shift Invariant Univariate Integral Operators." In Approximation Theory, 325–45. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1360-4_12.

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Anastassiou, George A., and Sorin G. Gal. "Differentiated Shift Invariant Multivariate Integral Operators." In Approximation Theory, 347–72. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1360-4_13.

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Anastassiou, George A., and Sorin G. Gal. "Generalized Shift Invariant Univariate Integral Operators." In Approximation Theory, 373–89. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1360-4_14.

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Anastassiou, George A., and Sorin G. Gal. "Generalized Shift Invariant Multivariate Integral Operators." In Approximation Theory, 391–400. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1360-4_15.

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Anastassiou, George A., and Sorin G. Gal. "Global Smoothness Preservation by Trigonometric Operators." In Approximation Theory, 203–10. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1360-4_5.

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Conference papers on the topic "APPROXIMATION OPERATORS"

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Shao, Yingchao, Zhengjiang Wu, and Keyun Qin. "Approximation Operators in Residuated Lattice." In 2010 International Conference on Web Information Systems and Mining (WISM). IEEE, 2010. http://dx.doi.org/10.1109/wism.2010.40.

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Bencsik, Attila, Barnabas Bede, Dan Noje, Hajime Nobuhara, and Kaoru Hirota. "Max product exponential approximation operators." In 2006 IEEE International Symposium on Industrial Electronics. IEEE, 2006. http://dx.doi.org/10.1109/isie.2006.295516.

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Rudas, I. J., B. Bede, H. Nobuhara, and K. Hirota. "On Approximation Capability of Pseudo-linear Shepard Approximation Operators." In 2006 IEEE International Conference on Fuzzy Systems. IEEE, 2006. http://dx.doi.org/10.1109/fuzzy.2006.1681876.

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Shao, Ming-Wen. "The Approximation Operators Within Formal Contexts." In 2007 International Conference on Multimedia and Ubiquitous Engineering (MUE'07). IEEE, 2007. http://dx.doi.org/10.1109/mue.2007.203.

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Zhao, Ming-qing, and Xiao-yan Zhao. "Axiomatization of Fuzzy Lower Approximation Operators." In 2006 International Conference on Machine Learning and Cybernetics. IEEE, 2006. http://dx.doi.org/10.1109/icmlc.2006.258938.

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Pagliani, P. "Information quanta and approximation spaces. I. Non-classical approximation operators." In 2005 IEEE International Conference on Granular Computing. IEEE, 2005. http://dx.doi.org/10.1109/grc.2005.1547363.

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Ge, Xun. "Granularity-Wise Separations in Covering Approximation Spaces with Some Approximation Operators." In 2008 International Symposium on Computer Science and Computational Technology. IEEE, 2008. http://dx.doi.org/10.1109/iscsct.2008.18.

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Buzura, O. A. "Filtering algorithms development using spline approximation operators." In 2012 International Conference and Exposition on Electrical and Power Engineering (EPE). IEEE, 2012. http://dx.doi.org/10.1109/icepe.2012.6463830.

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Reinov, Oleg I. "Approximation of p-summing operators by adjoints." In THE 5TH INTERNATIONAL CONFERENCE ON RESEARCH AND EDUCATION IN MATHEMATICS: ICREM5. AIP, 2012. http://dx.doi.org/10.1063/1.4724114.

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Louis, Anand. "Hypergraph Markov Operators, Eigenvalues and Approximation Algorithms." In STOC '15: Symposium on Theory of Computing. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2746539.2746555.

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Reports on the topic "APPROXIMATION OPERATORS"

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Brandt, Sebastian, Ralf Küsters, and Anni-Yasmin Turhan. Approximation and Difference in Description Logics. Aachen University of Technology, 2001. http://dx.doi.org/10.25368/2022.116.

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Abstract:
Approximation is a new inference service in Description Logics first mentioned by Baader, Küsters, and Molitor. Approximating a concept, defined in one Description Logic, means to translate this concept to another concept, defined in a second typically less expressive Description Logic, such that both concepts are as closely related as possible with respect to subsumption. The present paper provides the first in-depth investigation of this inference task. We prove that approximations from the Description Logic ALC to ALE always exist and propose an algorithm computing them. As a measure for the accuracy of the approximation, we introduce a syntax-oriented difference operator, which yields a concept description that contains all aspects of the approximated concept that are not present in the approximation. It is also argued that a purely semantical difference operator, as introduced by Teege, is less suited for this purpose. Finally, for the logics under consideration, we propose an algorithm computing the difference.
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Brent, Ronald. Theoretical and Numerical Validation of Scaler EM Propagation Modeling Using Parabolic Equations and the Pade Rational Operator Approximation. Fort Belvoir, VA: Defense Technical Information Center, October 2000. http://dx.doi.org/10.21236/ada386894.

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3

Goldberg, Moshe, and Marvin Marcus. Stability Analysis of Finite Difference Approximations to Hyperbolic Systems,and Problems in Applied and Computational Matrix and Operator Theory. Fort Belvoir, VA: Defense Technical Information Center, December 1990. http://dx.doi.org/10.21236/ada230543.

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4

Arhin, Stephen, Babin Manandhar, Kevin Obike, and Melissa Anderson. Impact of Dedicated Bus Lanes on Intersection Operations and Travel Time Model Development. Mineta Transportation Institute, June 2022. http://dx.doi.org/10.31979/mti.2022.2040.

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Over the years, public transit agencies have been trying to improve their operations by continuously evaluating best practices to better serve patrons. Washington Metropolitan Area Transit Authority (WMATA) oversees the transit bus operations in the Washington Metropolitan Area (District of Columbia, some parts of Maryland and Virginia). One practice attempted by WMATA to improve bus travel time and transit reliability has been the implementation of designated bus lanes (DBLs). The District Department of Transportation (DDOT) implemented a bus priority program on selected corridors in the District of Columbia leading to the installation of red-painted DBLs on corridors of H Street, NW, and I Street, NW. This study evaluates the impacts on the performance of transit buses along with the general traffic performance at intersections on corridors with DBLs installed in Washington, DC by using a “before” and “after” approach. The team utilized non-intrusive video data to perform vehicular turning movement counts to assess the traffic flow and delays (measures of effectiveness) with a traffic simulation software. Furthermore, the team analyzed the Automatic Vehicle Locator (AVL) data provided by WMATA for buses operating on the study segments to evaluate bus travel time. The statistical analysis showed that the vehicles traveling on H Street and I Street (NW) experienced significantly lower delays during both AM (7:00–9:30 AM) and PM (4:00–6:30 PM) peak hours after the installation of bus lanes. The approximation error metrics (normalized squared errors) for the testing dataset was 0.97, indicating that the model was predicting bus travel times based on unknown data with great accuracy. WMATA can apply this research to other segments with busy bus schedules and multiple routes to evaluate the need for DBLs. Neural network models can also be used to approximate bus travel times on segments by simulating scenarios with DBLs to obtain accurate bus travel times. Such implementation could not only improve WMATA’s bus service and reliability but also alleviate general traffic delays.
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