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'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Chebyshev approximation"

1

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
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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.
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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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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 present
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Hudyma, Uliana, та Vasyl Hnatyuk. "The Existence Conditions of the Extremality of the Admissible Element for the Problem of Finding the Generalized Сhebyshov’s Center of Several Points of Some Polynormated Space Relative to the Set of this Space". Mathematical and computer modelling. Series: Physical and mathematical sciences 25 (30 вересня 2024): 52–69. http://dx.doi.org/10.32626/2308-5878.2024-25.52-69.

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The problems related to the need to approximate complex mathematical objects in the best possible way with simpler and more convenient ones arise in various sections of mathematical science. An important class of approximation theory problems is the best simultaneous approximation of several elements. The problem of finding the Chebyshev center of several points of a linear normalized space relative to the set of this space can be attributed to the problems of best simultaneous approximation of several elements. This task consists in finding in a given set of linear normed space such a point (
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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 rat
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Morozov, Stanislav, Dmitry Zheltkov, and Alexander Osinsky. "Refining uniform approximation algorithm for low-rank Chebyshev embeddings." Russian Journal of Numerical Analysis and Mathematical Modelling 39, no. 5 (2024): 311–28. http://dx.doi.org/10.1515/rnam-2024-0027.

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Abstract Nowadays, low-rank approximations are a critical component of many numerical procedures. Traditionally the problem of low-rank approximation of matrices is solved in unitary invariant norms such as Frobenius or spectral norm due to the existence of efficient methods for constructing approximations. However, recent results discover the potential of low-rank approximations in the Chebyshev norm, which naturally arises in many applications. In this paper, we investigate the problem of uniform approximation of vectors, which is the main component in the low-rank approximations of matrices
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Polyakova, Lyudmila N. "Smooth approximations of nonsmooth convex functions." Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 18, no. 4 (2022): 535–47. http://dx.doi.org/10.21638/11701/spbu10.2022.408.

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For an arbitrary convex function, using the infimal convolution operation, a family of continuously differentiable convex functions approximating it is constructed. The constructed approximating family of smooth convex functions Kuratowski converges to the function under consideration. If the domain of the considered function is compact, then such smooth convex approximations are uniform in the Chebyshev metric. The approximation of a convex set by a family of smooth convex sets is also considered.
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Alharthi, M. R., Alvaro H. Salas, Wedad Albalawi, and S. A. El-Tantawy. "Novel Analytical and Numerical Approximations to the Forced Damped Parametric Driven Pendulum Oscillator: Chebyshev Collocation Method." Journal of Mathematics 2022 (June 22, 2022): 1–13. http://dx.doi.org/10.1155/2022/5454685.

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In this work, some novel approximate analytical and numerical solutions to the forced damped driven nonlinear (FDDN) pendulum equation and some relation equations of motion on the pivot vertically for arbitrary angles are obtained. The analytical approximation is derived in terms of the Jacobi elliptic functions with arbitrary elliptic modulus. For the numerical approximations, the Chebyshev collocation numerical method is introduced for analyzing the equation of motion. Moreover, the analytical approximation and numerical approximation using the Chebyshev collocation numerical method and the
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Khodier, Ahmed. "Perturbed Chebyshev rational approximation." International Journal of Computer Mathematics 80, no. 9 (2003): 1199–204. http://dx.doi.org/10.1080/0020716031000148520.

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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
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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 metho
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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
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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 espa
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Nudo, Frederico. "Approximations polynomiales et méthode des éléments finis enrichis, avec applications." Electronic Thesis or Diss., Pau, 2024. http://www.theses.fr/2024PAUU3067.

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Un problème très courant en science computationnelle est la détermination d'une approximation, dans un intervalle fixe, d'une fonction dont les évaluations ne sont connues que sur un ensemble fini de points. Une approche courante pour résoudre ce problème repose sur l'interpolation polynomiale. Un cas d'un grand intérêt pratique est celui où ces points suivent une distribution équidistante dans l'intervalle considéré. Dans ces hypothèses, un problème lié à l'interpolation polynomiale est le phénomène de Runge, caractérisé par une augmentation de l'erreur d'interpolation près des extrémités de
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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 sur
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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
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Books on the topic "Chebyshev approximation"

1

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. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1991.

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2

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

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Bernd, Fischer. Chebyshev polynomials are not always optimal. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1989.

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

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Freund, Roland W. On the constrained Chebyshev approximation problem on ellipses. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1988.

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Kowalski, Andrzej. Zastosowanie wielomianów Czebyszewa do analizy światłowodów cylindrycznych. 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. National Aeronautics and Space Administration, Langley Research Center, 1990.

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Freund, Roland W. New Bernstein type inequalitites for polynomials on ellipses. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1990.

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

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Research Institute for Advanced Computer Science (U.S.), ed. Explicitly solvable complex Chebyshev approximation problems related to sine polynomials. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1989.

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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. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-05228-7_5.

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2

Jongen, Hubertus Th, Peter Jonker, and Frank Twilt. "Chebyshev approximation, focal points." In Nonconvex Optimization and Its Applications. 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. 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. 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. 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. 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. 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. 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. 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. 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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Markiş, Iustin, Vlad Mihaly, Mircea Şuşcă, and Petru Dobra. "Convex Chebyshev Approximation for Descriptor Systems for Frequency Domain Data Fitting." In 2024 28th International Conference on System Theory, Control and Computing (ICSTCC). IEEE, 2024. http://dx.doi.org/10.1109/icstcc62912.2024.10744712.

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Ding, Qi, Alan V. Oppenheim, Petros T. Boufounos, et al. "Application of Weighted Chebyshev Approximation in Pulse Design for Quantum Gates." In 2024 IEEE Workshop on Signal Processing Systems (SiPS). IEEE, 2024. https://doi.org/10.1109/sips62058.2024.00024.

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Fang, Zeyu, and Jianlong Li. "A Stable Chebyshev-Padé Rational Approximation of Parabolic Equation Models for Underwater Sound Field Computation." In OCEANS 2024 - SINGAPORE. IEEE, 2024. http://dx.doi.org/10.1109/oceans51537.2024.10682403.

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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. 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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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), 1988. http://dx.doi.org/10.2172/6357493.

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