Relevant bibliographies by topics / Chebyshev approximation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Chebyshev approximation'

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Published: 4 June 2021
Last updated: 3 March 2023

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Journal articles on the topic "Chebyshev approximation"

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Malachivskyy, Petro. "Chebyshev approximation of the multivariable functions by some nonlinear expressions." Physico-mathematical modelling and informational technologies, no. 33 (September 2, 2021): 18–22. http://dx.doi.org/10.15407/fmmit2021.33.018.

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A method for constructing a Chebyshev approximation of the multivariable functions by exponential, logarithmic and power expressions is proposed. It consists in reducing the problem of the Chebyshev approximation by a nonlinear expression to the construction of an intermediate Chebyshev approximation by a generalized polynomial. The intermediate Chebyshev approximation by a generalized polynomial is calculated for the values of a certain functional transformation of the function we are approximating. The construction of the Chebyshev approximation of the multivariable functions by a polynomial is realized by an iterative scheme based on the method of least squares with a variable weight function.
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Jung, Soon-Mo, and Themistocles M. Rassias. "Approximation of Analytic Functions by Chebyshev Functions." Abstract and Applied Analysis 2011 (2011): 1–10. http://dx.doi.org/10.1155/2011/432961.

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Patseika, Pavel G., and Yauheni A. Rouba. "Fejer means of rational Fourier – Chebyshev series and approximation of function |x|s." Journal of the Belarusian State University. Mathematics and Informatics, no. 3 (November 29, 2019): 18–34. http://dx.doi.org/10.33581/2520-6508-2019-3-18-34.

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Approximation properties of Fejer means of Fourier series by Chebyshev – Markov system of algebraic fractions and approximation by Fejer means of function |x|s, 0 < s < 2, on the interval [−1,1], are studied. One orthogonal system of Chebyshev – Markov algebraic fractions is considers, and Fejer means of the corresponding rational Fourier – Chebyshev series is introduce. The order of approximations of the sequence of Fejer means of continuous functions on a segment in terms of the continuity module and sufficient conditions on the parameter providing uniform convergence are established. A estimates of the pointwise and uniform approximation of the function |x|s, 0 < s < 2, on the interval [−1,1], the asymptotic expressions under n→∞ of majorant of uniform approximations, and the optimal value of the parameter, which provides the highest rate of approximation of the studied functions are sums of rational use of Fourier – Chebyshev are found.
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Malachivskyy, P., L. Melnychok, and Ya Pizyur. "Chebyshev approximation of multivariable functions with the interpolation." Mathematical Modeling and Computing 9, no. 3 (2022): 757–66. http://dx.doi.org/10.23939/mmc2022.03.757.

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A method of constructing a Chebyshev approximation of multivariable functions by a generalized polynomial with the exact reproduction of its values at a given points is proposed. It is based on the sequential construction of mean-power approximations, taking into account the interpolation condition. The mean-power approximation is calculated using an iterative scheme based on the method of least squares with the variable weight function. An algorithm for calculating the Chebyshev approximation parameters with the interpolation condition for absolute and relative error is described. The presented results of solving test examples confirm the rapid convergence of the method when calculating the parameters of the Chebyshev approximation of tabular continuous functions of one, two and three variables with the reproduction of the values of the function at given points.
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Patseika, Pavel G., Yauheni A. Rouba, and Kanstantin A. Smatrytski. "On one rational integral operator of Fourier – Chebyshev type and approximation of Markov functions." Journal of the Belarusian State University. Mathematics and Informatics, no. 2 (July 30, 2020): 6–27. http://dx.doi.org/10.33581/2520-6508-2020-2-6-27.

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The purpose of this paper is to construct an integral rational Fourier operator based on the system of Chebyshev – Markov rational functions and to study its approximation properties on classes of Markov functions. In the introduction the main results of well-known works on approximations of Markov functions are present. Rational approximation of such functions is a well-known classical problem. It was studied by A. A. Gonchar, T. Ganelius, J.-E. Andersson, A. A. Pekarskii, G. Stahl and other authors. In the main part an integral operator of the Fourier – Chebyshev type with respect to the rational Chebyshev – Markov functions, which is a rational function of order no higher than n is introduced, and approximation of Markov functions is studied. If the measure satisfies the following conditions: suppμ = [1, a], a > 1, dμ(t) = ϕ(t)dt and ϕ(t) ἆ (t − 1)α on [1, a] the estimates of pointwise and uniform approximation and the asymptotic expression of the majorant of uniform approximation are established. In the case of a fixed number of geometrically distinct poles in the extended complex plane, values of optimal parameters that provide the highest rate of decreasing of this majorant are found, as well as asymptotically accurate estimates of the best uniform approximation by this method in the case of an even number of geometrically distinct poles of the approximating function. In the final part we present asymptotic estimates of approximation of some elementary functions, which can be presented by Markov functions.
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Khodier, Ahmed. "Perturbed Chebyshev rational approximation." International Journal of Computer Mathematics 80, no. 9 (September 2003): 1199–204. http://dx.doi.org/10.1080/0020716031000148520.

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Dunham, Charles B. "Chebyshev approximation by products." Journal of Approximation Theory 43, no. 4 (April 1985): 299–301. http://dx.doi.org/10.1016/0021-9045(85)90106-6.

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Sommariva, Alvise, Marco Vianello, and Renato Zanovello. "Adaptive Bivariate Chebyshev Approximation." Numerical Algorithms 38, no. 1 (March 2005): 79–94. http://dx.doi.org/10.1007/s11075-004-2859-y.

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Sommariva, Alvise, Marco Vianello, and Renato Zanovello. "Adaptive bivariate Chebyshev approximation." Numerical Algorithms 38, no. 1-3 (March 2005): 79–94. http://dx.doi.org/10.1007/bf02810617.

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Niu, Cuixia, Huiqing Liao, Heping Ma, and Hua Wu. "Approximation Properties of Chebyshev Polynomials in the Legendre Norm." Mathematics 9, no. 24 (December 16, 2021): 3271. http://dx.doi.org/10.3390/math9243271.

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In this paper, we present some important approximation properties of Chebyshev polynomials in the Legendre norm. We mainly discuss the Chebyshev interpolation operator at the Chebyshev–Gauss–Lobatto points. The cases of single domain and multidomain for both one dimension and multi-dimensions are considered, respectively. The approximation results in Legendre norm rather than in the Chebyshev weighted norm are given, which play a fundamental role in numerical analysis of the Legendre–Chebyshev spectral method. These results are also useful in Clenshaw–Curtis quadrature which is based on sampling the integrand at Chebyshev points.
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Dissertations / Theses on the topic "Chebyshev approximation"

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Park, Jae H. "Chebyshev Approximation of Discrete polynomials and Splines." Diss., Virginia Tech, 1999. http://hdl.handle.net/10919/30195.

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The recent development of the impulse/summation approach for efficient B-spline computation in the discrete domain should increase the use of B-splines in many applications. Because we show here how the impulse/summation approach can also be used for constructing polynomials, the approach with a search table approach for the inverse square root operation allows an efficient shading algorithm for rendering an image in a computer graphics system. The approach reduces the number of multiplies and makes it possible for the entire rendering process to be implemented using an integer processor. In many applications, Chebyshev approximation with polynomials and splines is useful in representing a stream of data or a function. Because the impulse/summation approach is developed for discrete systems, some aspects of traditional continuous approximation are not applicable. For example, the lack of the continuity concept in the discrete domain affects the definition of the local extrema of a function. Thus, the method of finding the extrema must be changed. Both forward differences and backward differences must be checked to find extrema instead of using the first derivative in the continuous domain approximation. Polynomial Chebyshev approximation in the discrete domain, just as in the continuous domain, forms a Chebyshev system. Therefore, the Chebyshev approximation process always produces a unique best approximation. Because of the non-linearity of free knot polynomial spline systems, there may be more than one best solution and the convexity of the solution space cannot be guaranteed. Thus, a Remez Exchange Algorithm may not produce an optimal approximation. However, we show that the discrete polynomial splines approximate a function using a smaller number of parameters (for a similar minimax error) than the discrete polynomials do. Also, the discrete polynomial spline requires much less computation and hardware than the discrete polynomial for curve generation when we use the impulse/summation approach. This is demonstrated using two approximated FIR filter implementations.
Ph. D.
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Chit, Nassim N. "Weighted Chebyshev complex-valued approximation for FIR digital filters." Thesis, Swansea University, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.278340.

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Taylor, Barbara J. "Chebyshev centers and best simultaneous approximation in normed linear spaces." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63872.

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Pachon, Ricardo. "Algorithms for polynomial and rational approximation." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:f268a835-46ef-45ea-8610-77bf654b9442.

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Robust algorithms for the approximation of functions are studied and developed in this thesis. Novel results and algorithms on piecewise polynomial interpolation, rational interpolation and best polynomial and rational approximations are presented. Algorithms for the extension of Chebfun, a software system for the numerical computation with functions, are described. These algorithms allow the construction and manipulation of piecewise smooth functions numerically with machine precision. Breakpoints delimiting subintervals are introduced explicitly, implicitly or automatically, the latter method combining recursive subdivision and edge detection techniques. For interpolation by rational functions with free poles, a novel method is presented. When the interpolation nodes are roots of unity or Chebyshev points the algorithm is particularly simple and relies on discrete Fourier transform matrices, which results in a fast implementation using the Fast Fourier Transform. The method is generalised for arbitrary grids, which requires the construction of polynomials orthogonal on the set of interpolation nodes. The new algorithm has connections with other methods, particularly the work of Jacobi and Kronecker, Berrut and Mittelmann, and Egecioglu and Koc. Computed rational interpolants are compared with the behaviour expected from the theory of convergence of these approximants, and the difficulties due to truncated arithmetic are explained. The appearance of common factors in the numerator and denominator due to finite precision arithmetic is characterised by the behaviour of the singular values of the linear system associated with the rational interpolation problem. Finally, new Remez algorithms for the computation of best polynomial and rational approximations are presented. These algorithms rely on interpolation, for the computation of trial functions, and on Chebfun, for the location of trial references. For polynomials, the algorithm is particularly robust and efficient, and we report experiments with degrees in the thousands. For rational functions, we clarify the numerical issues that affect its application.
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Filip, Silviu-Ioan. "Robust tools for weighted Chebyshev approximation and applications to digital filter design." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEN063/document.

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De nombreuses méthodes de traitement du signal reposent sur des résultats puissants d'approximation numérique. Un exemple significatif en est l'utilisation de l'approximation de type Chebyshev pour l'élaboration de filtres numériques.En pratique, le caractère fini des formats numériques utilisés en machine entraîne des difficultés supplémentaires pour la conception de filtres numériques (le traitement audio et le traitement d'images sont deux domaines qui utilisent beaucoup le filtrage). La majorité des outils actuels de conception de filtres ne sont pas optimisés et ne certifient pas non plus la correction de leurs résultats. Notre travail se veut un premier pas vers un changement de cette situation.La première partie de la thèse traite de l'étude et du développement de méthodes relevant de la famille Remez/Parks-McClellan pour la résolution de problèmes d'approximation polynomiale de type Chebyshev, en utilisant l'arithmétique virgule-flottante.Ces approches sont très robustes, tant du point de vue du passage à l'échelle que de la qualité numérique, pour l'élaboration de filtres à réponse impulsionnelle finie (RIF).Cela dit, dans le cas des systèmes embarqués par exemple, le format des coefficients du filtre qu'on utilise en pratique est beaucoup plus petit que les formats virgule flottante standard et d'autres approches deviennent nécessaires.Nous proposons une méthode (quasi-)optimale pour traîter ce cas. Elle s'appuie sur l'algorithme LLL et permet de traiter des problèmes de taille bien supérieure à ceux que peuvent traiter les approches exactes. Le résultat est ensuite utilisé dans une couche logicielle qui permet la synthèse de filtres RIF pour des circuits de type FPGA.Les résultats que nous obtenons en sortie sont efficaces en termes de consommation d'énergie et précis. Nous terminons en présentant une étude en cours sur les algorithmes de type Remez pour l'approximation rationnelle. Ce type d'approches peut être utilisé pour construire des filtres à réponse impulsionnelle infinie (RII) par exemple. Nous examinons les difficultés qui limitent leur utilisation en pratique
The field of signal processing methods and applications frequentlyrelies on powerful results from numerical approximation. One suchexample, at the core of this thesis, is the use of Chebyshev approximationmethods for designing digital filters.In practice, the finite nature of numerical representations adds an extralayer of difficulty to the design problems we wish to address using digitalfilters (audio and image processing being two domains which rely heavilyon filtering operations). Most of the current mainstream tools for thisjob are neither optimized, nor do they provide certificates of correctness.We wish to change this, with some of the groundwork being laid by thepresent work.The first part of the thesis deals with the study and development ofRemez/Parks-McClellan-type methods for solving weighted polynomialapproximation problems in floating-point arithmetic. They are veryscalable and numerically accurate in addressing finite impulse response(FIR) design problems. However, in embedded and power hungry settings,the format of the filter coefficients uses a small number of bits andother methods are needed. We propose a (quasi-)optimal approach basedon the LLL algorithm which is more tractable than exact approaches.We then proceed to integrate these aforementioned tools in a softwarestack for FIR filter synthesis on FPGA targets. The results obtainedare both resource consumption efficient and possess guaranteed accuracyproperties. In the end, we present an ongoing study on Remez-type algorithmsfor rational approximation problems (which can be used for infinite impulseresponse (IIR) filter design) and the difficulties hindering their robustness
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Melkemi, Khaled. "Orthogonalité des B-splines de Chebyshev cardinales dans un espace de Sobolev pondéré." Phd thesis, Université Joseph Fourier (Grenoble), 1999. http://tel.archives-ouvertes.fr/tel-00004843.

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Ce travail porte sur l'étude théorique et numérique des splines de Chebyshev. Ces fonctions généralisent les splines polynomiales tout en préservant l'essentiel de leurs propriétés. Elles offrent de plus un intérêt particulier pour le design géométrique grâce aux paramètres de forme qu'elles fournissent. Dans un premier temps, nous étudions les splines basées sur un espace de Chebyshev invariant par translations, et les propriétés de la B-spline correspondante. Dans un deuxième temps, nous montrons, sous certaines hypothèses, que la base des B-splines de Chebyshev est orthonormale dans un espace de Sobolev pondéré par une suite unique de nombres positifs. La meilleure approximation dans l'espace de splines de Chebyshev au sens de la norme associé au produit scalaire précédent est alors un projecteur local. Enfin, pour l'implémentation numérique des résultats précédents, nous utilisons une méthode de quadratures adaptées. Quelques exemples illustrant les effets de forme obtenus sont présentés. Ces résultats généralisent un résultat prouvé récemment par Ulrich Reif dans le cas particulier des splines polynomiales.
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Johnson, William Joel Dietmar. "Rational fraction approximations for passive network functions." [Tampa, Fla.] : University of South Florida, 2005. http://purl.fcla.edu/fcla/etd/SFE0001083.

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Masson, Yannick. "Existence et construction de réseaux de Chebyshev avec singularités et application aux gridshells." Thesis, Paris Est, 2017. http://www.theses.fr/2017PESC1144/document.

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Les réseaux de Chebyshev sont des systèmes de coordonnées sur les surfaces que l'on obtient par cisaillement d'un domaine du plan. Ceux-ci sont utilisés en particulier pour modéliser les gridshells qui constituent une construction architecturale notamment reconnue pour son faible coût environnemental. La difficulté principale dans la conception des gridshells est le manque de diversité des formes accessibles. En effet, bien que toute surface admette localement en tout point un réseau de Chebyshev, l'existence globale de ce type de coordonnées n'est possible que sur un ensemble restreint de surfaces. La recherche de conditions suffisantes pour l'existence globale de réseaux de Chebyshev est toujours d'actualité. Un des résultats de cette thèse est l'amélioration de ces conditions. Les possibilités d'améliorations en ce sens étant néanmoins limitées, nous élargissons la perspective en considérant des réseaux de Chebyshev avec singularités. Notre résultat principal est l'existence de réseaux de Chebyshev avec singularités coniques, lisses par morceaux, sur toute surface dont la courbure totale positive est inférieure à $2pi$ et dont la courbure totale négative est finie. Notre preuve est constructive, ce qui permet de déterminer ces réseaux dans des cas pratiques. Nous avons implémenté un cas particulier de notre algorithme dans le logiciel Rhinoceros et nous présentons des exemples de réseaux construits par cette méthode
Chebyshev nets are coordinate systems on surfaces obtained by pure shearing of a planar domain.These nets are used in particular to model gridshells, an architectural construction which is well-known for its low environmental impact. The main issue when designing a gridshell is the lack of diversityof the accessible shapes. Indeed, although any surface admits locally a Chebyshev net at any point, the global existence for these coordinate systems is only possible for a restricted set of surfaces. The research for sufficient conditions ensuring the global existence of Chebyshev nets is still ongoing. A result achieved in this thesis is an improvement on these conditions. Since the improvement in this direction seems to be rather limited, we broaden the perspective by introducing Chebyshev nets with singularities. Our main result is the existence of a global Chebyshev net with conical singularities on any surface with total positive curvature less than $2pi$ and with finite total negative curvature. Our proof is constructive, so that this method can be applied to practical cases. We have implemented a special instance of this algorithm in the software Rhinoceros and some discrete Chebyshev nets constructed using this method are presented
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Essakhi, Brahim. "Modélisation électromagnétique 3D sur une large bande de fréquences par combinaison d'une méthode d'éléments finis et d'une approximation par fractions rationnelles : application aux structures rayonnantes." Paris 11, 2005. http://www.theses.fr/2005PA112151.

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Les outils de simulation numérique connaissent une utilisation intensive dans la résolution des problèmes de CEM. L'une des raisons est que la complexité croissante des problèmes à étudier rend l'expérimentation difficile à réaliser. De plus, les mesures ne peuvent être faites qu'en un nombre restreint de points de l'espace. La méthode des éléments finis a pour avantages de pouvoir aisément prendre en compte des géométries complexes et des milieux hétérogènes. Elle utilise un maillage conforme, qui s'adapte à la géométrie de la structure analysée et qui permet des raffinements locaux dans les régions où les variations des propriétés physiques, géométriques ou des champs sont plus importantes. Une formulation temporelle permet l'analyse de problèmes directement dans le domaine du temps. Une formulation fréquentielle conduit à résoudre un système linéaire pour chaque fréquence d'étude. Dans de nombreuses applications, les quantités électromagnétiques doivent être déterminées sur une large bande de fréquences et le système linéaire doit être résolu pour chaque fréquence d'intérêt. Ceci entraîne un coût de calcul important. Une alternative consiste à rechercher une approximation de la solution sous forme d'un développement en série ou d'une fraction rationnelle. Une approche possible consiste à développer la solution en série de Taylor autour d'une fréquence centrale. Le rayon de convergence de la série est limité mais il est possible d'étendre cet intervalle de validité en recourant à une approximation rationnelle de Padé. Une autre méthode consiste à rechercher une interpolation de la solution par fractions rationnelles, il s'agit de l'approximation de Chebyshev
The tools for digital simulation know an intensive use in the resolution of the problems of CEM. One of the reasons is that the increasing complexity of the problems to be studied makes the experimentation difficult to realize. Moreover, measurements cannot be made that in a restricted number of points of space. The finite element method has the advantages of easily being able to take into account complex geometries and heterogeneous mediums. It uses a grid in conformity, which adapts to the geometry of the analyzed structure and which allows local refinements in the areas where variations of the physical properties, geometrical or of the fields are more significant. A temporal formulation allows the analysis of problems directly in the field of time. A frequential formulation results in solving a linear system for each frequency of study. In many applications, the electromagnetic quantities must be given on a broad frequency band and the linear system must be solved for each frequency of interest. This involves a cost of significant calculation. An alternative consists in seeking an approximation of the solution in the form of a development in series or of a rational fraction. A possible approach consists in developing the solution in Taylor series around a centre frequency. The interval of convergence of the series is limited but it is possible to extend this interval of validity while resorting to a rational approximation of Padé. The approximation of Chebyshev is an other method based on rational approximation, it consists in seeking an interpolation of the solution
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Midgley, Stuart. "Quantum waveguide theory." University of Western Australia. School of Physics, 2003. http://theses.library.uwa.edu.au/adt-WU2004.0036.

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The study of nano-electronic devices is fundamental to the advancement of the semiconductor industry. As electronic devices become increasingly smaller, they will eventually move into a regime where the classical nature of the electrons no longer applies. As the quantum nature of the electrons becomes increasingly important, classical or semiclassical theories and methods will no longer serve their purpose. For example, the simplest non-classical effect that will occur is the tunnelling of electrons through the potential barriers that form wires and transistors. This results in an increase in noise and a reduction in the device?s ability to function correctly. Other quantum effects include coulomb blockade, resonant tunnelling, interference and diffraction, coulomb drag, resonant blockade and the list goes on. This thesis develops both a theoretical model and computational method to allow nanoelectronic devices to be studied in detail. Through the use of computer code and an appropriate model description, potential problems and new novel devices may be identified and studied. The model is as accurate to the physical realisation of the devices as possible to allow direct comparison with experimental outcomes. Using simple geometric shapes of varying potential heights, simple devices are readily accessible: quantum wires; quantum transistors; resonant cavities; and coupled quantum wires. Such devices will form the building blocks of future complex devices and thus need to be fully understood. Results obtained studying the connection of a quantum wire with its surroundings demonstrate non-intuitive behaviour and the importance of device geometry to electrical characteristics. The application of magnetic fields to various nano-devices produced a range of interesting phenomenon with promising novel applications. The magnetic field can be used to alter the phase of the electron, modifying the interaction between the electronic potential and the transport electrons. This thesis studies in detail the Aharonov-Bohm oscillation and impurity characterisation in quantum wires. By studying various devices considerable information can be added to the knowledge base of nano-electronic devices and provide a basis to further research. The computational algorithms developed in this thesis are highly accurate, numerically efficient and unconditionally stable, which can also be used to study many other physical phenomena in the quantum world. As an example, the computational algorithms were applied to positron-hydrogen scattering with the results indicating positronium formation.
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Books on the topic "Chebyshev approximation"

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Alex, Solomonoff, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., eds. Accuracy and speed in computing the Chebyshev collocation derivative. [Washington, DC]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1991.

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Rivlin, Theodore J. Chebyshev polynomials: From approximation theory toalgebra and number theory. 2nd ed. New York: Wiley, 1990.

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Bernd, Fischer. Chebyshev polynomials are not always optimal. [Moffett Field, CA]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1989.

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Freund, Roland W. On the constrained Chebyshev approximation problem on ellipses. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1988.

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Rivlin, Theodore J. Chebyshev polynomials: From approximation theory to algebra and number theory. 2nd ed. New York: Wiley, 1990.

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Some investigations in minimax estimation theory. Warszawa: Państwowe Wydawn. Nauk., 1985.

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Freund, Roland W. New Bernstein type inequalitites for polynomials on ellipses. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1990.

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Kowalski, Andrzej. Zastosowanie wielomianów Czebyszewa do analizy światłowodów cylindrycznych. Warszawa: Wydawnictwa Politdchniki Warszawskiej, 1992.

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Hillel, Tal-Ezer, and Langley Research Center, eds. Modified Chebyshev pseudospectral method with O (N) time step restriction. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1990.

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Németh, Géza. Mathematical approximation of special functions: Ten papers on Chebyshev expansions. New York: Nova Science Publishers, 1992.

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Book chapters on the topic "Chebyshev approximation"

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Iske, Armin. "Chebyshev Approximation." In Approximation Theory and Algorithms for Data Analysis, 139–84. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-05228-7_5.

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Jongen, Hubertus Th, Peter Jonker, and Frank Twilt. "Chebyshev approximation, focal points." In Nonconvex Optimization and Its Applications, 155–205. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-0017-9_4.

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Nürnberger, Günther. "Polynomials and Chebyshev Spaces." In Approximation by Spline Functions, 1–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-61342-5_1.

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Braess, Dietrich. "Chebyshev Approximation by γ-Polynomials." In Nonlinear Approximation Theory, 181–220. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-61609-9_7.

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Nürnberger, Günther. "Splines and Weak Chebyshev Spaces." In Approximation by Spline Functions, 80–189. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-61342-5_2.

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Deutsch, Frank. "Convexity of Chebyshev Sets." In Best Approximation in Inner Product Spaces, 301–9. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4684-9298-9_12.

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Nürnberger, Günther. "Strong Unicity Constants in Chebyshev Approximation." In Numerical Methods of Approximation Theory/Numerische Methoden der Approximationstheorie, 144–54. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-6656-9_13.

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Sukhorukova, Nadezda, Julien Ugon, and David Yost. "Chebyshev Multivariate Polynomial Approximation: Alternance Interpretation." In MATRIX Book Series, 177–82. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-72299-3_8.

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Tang, P. T. P. "A fast algorithm for linear complex Chebyshev approximation." In Algorithms for Approximation II, 265–73. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4899-3442-0_24.

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Watson, G. A. "Numerical methods for Chebyshev approximation of complex-valued functions." In Algorithms for Approximation II, 246–64. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4899-3442-0_23.

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Conference papers on the topic "Chebyshev approximation"

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Sadeghian, Masoud, and James E. Stine. "Optimized low-power elementary function approximation for Chebyshev series approximations." In 2012 46th Asilomar Conference on Signals, Systems and Computers. IEEE, 2012. http://dx.doi.org/10.1109/acssc.2012.6489169.

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Zagorowska, Marta, and Nina Thornhill. "Compressor map approximation using Chebyshev polynomials." In 2017 25th Mediterranean Conference on Control and Automation (MED). IEEE, 2017. http://dx.doi.org/10.1109/med.2017.7984228.

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Yadav, Om Prakash, and Shashwati Ray. "Efficient ECG Approximation Using Chebyshev Polynomials." In 2018 International Conference on Inventive Research in Computing Applications (ICIRCA). IEEE, 2018. http://dx.doi.org/10.1109/icirca.2018.8597372.

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Clemente, Carmine, and John J. Soraghan. "Bistatic slant range approximation using Chebyshev Polynomials." In 2011 IEEE Radar Conference (RadarCon). IEEE, 2011. http://dx.doi.org/10.1109/radar.2011.5960645.

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Shuman, David I., Pierre Vandergheynst, and Pascal Frossard. "Chebyshev polynomial approximation for distributed signal processing." In 2011 International Conference on Distributed Computing in Sensor Systems (DCOSS). IEEE, 2011. http://dx.doi.org/10.1109/dcoss.2011.5982158.

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Abutheraa, Mohammed A., and David Lester. "Machine-efficient Chebyshev approximation for exact arithmetic." In the 2010 Spring Simulation Multiconference. New York, New York, USA: ACM Press, 2010. http://dx.doi.org/10.1145/1878537.1878625.

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Onuki, Masaki, Yuichi Tanaka, and Masahiro Okuda. "Improved eigenvalue shrinkage using weighted Chebyshev polynomial approximation." In 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2017. http://dx.doi.org/10.1109/icassp.2017.7953016.

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Alkhairy, A., K. Christian, and J. Lim. "Design of FIR filters by complex Chebyshev approximation." In [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing. IEEE, 1991. http://dx.doi.org/10.1109/icassp.1991.150787.

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Jeong, Yi-Ru, Ic-Pyo Hong, Heoung-Jae Chun, Yong Bae Park, Youn-Jae Kim, and Jong-Gwan Yook. "Fast analysis over a wide band using Chebyshev approximation with Clenshaw-Lord approximation." In 2014 8th European Conference on Antennas and Propagation (EuCAP). IEEE, 2014. http://dx.doi.org/10.1109/eucap.2014.6902029.

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Kadambari, Sai Kiran, Robin Francis, and Sundeep Prabhakar Chepuri. "Distributed Denoising over Simplicial Complexes using Chebyshev Polynomial Approximation." In 2022 30th European Signal Processing Conference (EUSIPCO). IEEE, 2022. http://dx.doi.org/10.23919/eusipco55093.2022.9909593.

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Reports on the topic "Chebyshev approximation"

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Tang, Ping Tak Peter. Strong uniqueness of best complex Chebyshev approximation to analytic perturbations of analytic function. Office of Scientific and Technical Information (OSTI), March 1988. http://dx.doi.org/10.2172/6357493.

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