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Journal articles on the topic 'Chebyshev approximation'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 March 2023

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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 is realized by an iterative scheme based on the method of least squares with a variable weight function.

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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

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 MATHEMATICA command Fit are compared with the Runge–Kutta (RK) numerical solution. Also, the maximum distance error to all obtained approximations is estimated with respect to the RK numerical solution. The obtained results help many authors to understand the mechanism of many phenomena related to the plasma physics, classical mechanics, quantum mechanics, optical fiber, and electronic circuits.

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12

Gu, Le Min. "P-Least Squares Method of Curve Fitting." Advanced Materials Research 699 (May 2013): 885–92. http://dx.doi.org/10.4028/www.scientific.net/amr.699.885.

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P-Least Squares (P-LS) method is Least Squares (LS) method promotion, based on the criteria of error -squares minimal to select parameter , namely satisfies following constitute the curve-fitting method. Due to the arbitrariness of the number , P-LS method has a wide field of application, when , P-LS approximation translated Chebyshev optimal approximation. This paper discusses the general principles of P-LS method; provides a way to realize the general solution of P-LS approximation. P-Least Squares method not only has significantly reduces the maximum error, also has solved the problems of Chebyshev approximation non-solution in some complex non-linear approximations，and also has the computation conveniently, can carry on the large-scale multi-data processing ability. This method is introduced by some examples unified in the materials science, the chemical engineering and the life body change.

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13

Melnychok, Lev. "Chebyshev approximation of functions of two variables by a rational expression with interpolation." Physico-mathematical modelling and informational technologies, no. 33 (September 3, 2021): 33–39. http://dx.doi.org/10.15407/fmmit2021.33.033.

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A method for constructing a Chebyshev approximation by a rational expression with interpolation for functions of two variables is proposed The idea of the method is based on the construction of the ultimate mean-power approximation in the norm of space Lp at p¬∞ . An iterative scheme based on the least squares method with two variable weight functions was used to construct such a Chebyshev approximation. The results of test examples confirm the effectiveness of the proposed method for constructing the Chebyshev approximation by a rational expression with interpolation.

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14

Zhou, Xiaolin, and Qun Lin. "Chebyshev Biorthogonal Multiwavelets and Approximation." Journal of Applied Mathematics and Physics 09, no. 02 (2021): 233–41. http://dx.doi.org/10.4236/jamp.2021.92017.

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15

Dunham, Charles B. "Nearby Chebyshev (powered) rational approximation." Journal of Approximation Theory 60, no. 1 (January 1990): 31–42. http://dx.doi.org/10.1016/0021-9045(90)90071-w.

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16

Patseika, P. G., and Y. A. Rouba. "The Abel – Poisson means of conjugate Fourier – Chebyshev series and their approximation properties." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 57, no. 2 (July 16, 2021): 156–75. http://dx.doi.org/10.29235/1561-2430-2021-57-2-156-175.

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Herein, the approximation properties of the Abel – Poisson means of rational conjugate Fourier series on the system of the Chebyshev–Markov algebraic fractions are studied, and the approximations of conjugate functions with density | x |s , s ∈(1, 2), on the segment [–1,1] by this method are investigated. In the introduction, the results related to the study of the polynomial and rational approximations of conjugate functions are presented. The conjugate Fourier series on one system of the Chebyshev – Markov algebraic fractions is constructed. In the main part of the article, the integral representation of the approximations of conjugate functions on the segment [–1,1] by the method under study is established, the asymptotically exact upper bounds of deviations of conjugate Abel – Poisson means on classes of conjugate functions when the function satisfies the Lipschitz condition on the segment [–1,1] are found, and the approximations of the conjugate Abel – Poisson means of conjugate functions with density | x |s , s ∈(1, 2), on the segment [–1,1] are studied. Estimates of the approximations are obtained, and the asymptotic expression of the majorant of the approximations in the final part is found. The optimal value of the parameter at which the greatest rate of decreasing the majorant is provided is found. As a consequence of the obtained results, the problem of approximating the conjugate function with density | x |s , s ∈(1, 2), by the Abel – Poisson means of conjugate polynomial series on the system of Chebyshev polynomials of the first kind is studied in detail. Estimates of the approximations are established, as well as the asymptotic expression of the majorants of the approximations. This work is of both theoretical and applied nature. It can be used when reading special courses at mathematical faculties and for solving specific problems of computational mathematics.

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17

Patseika, P. G., and Y. A. Rovba. "On approximations of the function |x|^s by the Vallee Poussin means of the Fourier series by the system of the Chebyshev – Markov rational fractions." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 3 (October 7, 2019): 263–82. http://dx.doi.org/10.29235/1561-2430-2019-55-3-263-282.

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The approximative properties of the Valle Poussin means of the Fourier series by the system of the Chebyshev – Markov rational fractions in the approximation of the function |x|s, 0 < s < 2 are investigated. The introduction presents the main results of the previously known works on the Vallee Poussin means in the polynomial and rational cases, as well as on the known literature data on the approximations of functions with power singularity. The Valle Poussin means on the interval [–1,1] as a method of summing the Fourier series by one system of the Chebyshev – Markov rational fractions are introduced. In the main section of the article, a integral representation for the error of approximations by the rational Valle Poussin means of the function |x|s, 0 < s < 2, on the segment [–1,1], an estimate of deviations of the Valle Poussin means from the function |x|s, 0 < s < 2, depending on the position of the point on the segment, a uniform estimate of deviations on the segment [–1,1] and its asymptotic expression are found. The optimal value of the parameter is obtained, at which the deviation error of the Valle Poussin means from the function |x|s, 0 < s <2, on the interval [–1,1] has the highest velocity of zero. As a consequence of the obtained results, the problem of approximation of the function |x|s, s > 0, by the Valle Poussin means of the Fourier series by the system of the Chebyshev first-kind polynomials is studied in detail. The pointwise estimation of approximation and asymptotic estimation are established.The work is both theoretical and applied. Its results can be used to read special courses at mathematical faculties and to solve specific problems of computational mathematics.

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18

Kowynia, Joanna. "The unicity of best approximation in a space of compact operators." MATHEMATICA SCANDINAVICA 108, no. 1 (March 1, 2011): 146. http://dx.doi.org/10.7146/math.scand.a-15164.

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Chebyshev subspaces of $\mathcal{K}(c_0,c_0)$ are studied. A $k$-dimensional non-interpolating Chebyshev subspace is constructed. The unicity of best approximation in non-Chebyshev subspaces is considered.

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19

Wang, Lidan, Meitao Duan, and Shukai Duan. "Memristive Chebyshev Neural Network and Its Applications in Function Approximation." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/429402.

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A novel Chebyshev neural network combined with memristors is proposed to perform the function approximation. The relationship between memristive conductance and weight update is derived, and the model of a single-input memristive Chebyshev neural network is established. Corresponding BP algorithm and deriving algorithm are introduced to the memristive Chebyshev neural networks. Their advantages include less model complexity, easy convergence of the algorithm, and easy circuit implementation. Through the MATLAB simulation results, we verify the feasibility and effectiveness of the memristive Chebyshev neural networks.

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20

Foupouagnigni, Mama, Daniel Duviol Tcheutia, Wolfram Koepf, and Kingsley Njem Forwa. "Approximation by interpolation: the Chebyshev nodes." Journal of Classical Analysis, no. 1 (2020): 39–53. http://dx.doi.org/10.7153/jca-2020-17-04.

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21

Foupouagnigni, Mama, Daniel Duviol Tcheutia, Wolfram Koepf, and Kingsley Njem Forwa. "Approximation by interpolation: the Chebyshev nodes." Journal of Classical Analysis, no. 1 (2021): 39–53. http://dx.doi.org/10.7153/jca-2021-17-04.

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22

Kroo, Andras. "Chebyshev Rank in L 1 -Approximation." Transactions of the American Mathematical Society 296, no. 1 (July 1986): 301. http://dx.doi.org/10.2307/2000575.

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23

Dolgov, Sergey, Daniel Kressner, and Christoph Strössner. "Functional Tucker Approximation Using Chebyshev Interpolation." SIAM Journal on Scientific Computing 43, no. 3 (January 2021): A2190—A2210. http://dx.doi.org/10.1137/20m1356944.

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24

Yannacopoulos, A. N., J. Brindley, J. H. Merkin, and M. J. Pilling. "Approximation of attractors using Chebyshev polynomials." Physica D: Nonlinear Phenomena 99, no. 2-3 (December 1996): 162–74. http://dx.doi.org/10.1016/s0167-2789(96)00164-9.

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25

Li, Chong, and G. A. Watson. "On nonlinear simultaneous Chebyshev approximation problems." Journal of Mathematical Analysis and Applications 288, no. 1 (December 2003): 167–81. http://dx.doi.org/10.1016/s0022-247x(03)00589-4.

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26

Feng, Guohui. "A counterexample on global Chebyshev approximation." Journal of Approximation Theory 51, no. 2 (October 1987): 93–97. http://dx.doi.org/10.1016/0021-9045(87)90023-2.

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27

Changzhong, Zhu, and Charles B. Dunham. "Biased varisolvent Chebyshev approximation on subsets." Journal of Approximation Theory 55, no. 1 (October 1988): 12–17. http://dx.doi.org/10.1016/0021-9045(88)90106-2.

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28

Brosowski, Bruno, and Claudia Guerreiro. "Stability of best rational Chebyshev approximation." Journal of Approximation Theory 61, no. 3 (June 1990): 279–321. http://dx.doi.org/10.1016/0021-9045(90)90009-f.

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29

Alimov, A. L. "Piecewise Chebyshev approximation of experimental data." USSR Computational Mathematics and Mathematical Physics 26, no. 6 (January 1986): 102–7. http://dx.doi.org/10.1016/0041-5553(86)90157-6.

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30

Brannigan, Michael. "Discrete Chebyshev Approximation with Linear Constraints." SIAM Journal on Numerical Analysis 22, no. 1 (February 1985): 1–15. http://dx.doi.org/10.1137/0722001.

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31

Malachivskyy, P. S., Ya V. Pizyur, N. V. Danchak, and E. B. Orazov. "Chebyshev Approximation by Exponential-Power Expression." Cybernetics and Systems Analysis 49, no. 6 (November 2013): 877–81. http://dx.doi.org/10.1007/s10559-013-9577-1.

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32

Wu, Shengwei, Jiarui Zhao, Yanyan Xu, Guanggui Chen, and Na Cheng. "The Chebyshev Set Problem in Riesz Space." Journal of Function Spaces 2022 (March 30, 2022): 1–8. http://dx.doi.org/10.1155/2022/4343472.

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In this paper, we mainly study the best approximation theory in Riesz space, which is not constructed by the norm, but only rely on the order structure. Based on the order structure, we propose the concept of the order best approximation in Riesz space and discuss some problems related to the order best approximation, including some sufficient and necessary conditions for satisfying the order best approximation set. Finally, we consider the order best approximation projection and its related properties.

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33

Goudarzi, H. R. "On the Uniqueness of p-Best Approximation in Probabilistic Normed Spaces." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 5 (July 26, 2018): 475–80. http://dx.doi.org/10.1515/ijnsns-2016-0127.

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AbstractThe main aim of this paper is to present some basic as well as essential results involving the notion of p-Chebyshev sets in probabilistic normed spaces. In particular, we discuss the convexity of p-Chebyshev sets, decomposition of the space into its special subspaces, and we see a characterization of p-Chebyshev sets in quotient spaces.

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34

Journal, Baghdad Science. "Orthogonal Functions Solving Linear functional Differential EquationsUsing Chebyshev Polynomial." Baghdad Science Journal 5, no. 1 (March 2, 2008): 143–48. http://dx.doi.org/10.21123/bsj.5.1.143-148.

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A method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.

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35

van den Berg, Jan Bouwe, and Ray Sheombarsing. "Rigorous numerics for ODEs using Chebyshev series and domain decomposition." Journal of Computational Dynamics 8, no. 3 (2021): 353. http://dx.doi.org/10.3934/jcd.2021015.

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<p style='text-indent:20px;'>In this paper we present a rigorous numerical method for validating analytic solutions of nonlinear ODEs by using Chebyshev-series and domain decomposition. The idea is to define a Newton-like operator, whose fixed points correspond to solutions of the ODE, on the space of geometrically decaying Chebyshev coefficients, and to use the so-called radii-polynomial approach to prove that the operator has an isolated fixed point in a small neighborhood of a numerical approximation. The novelty of the proposed method is the use of Chebyshev series in combination with domain decomposition. In particular, a heuristic procedure based on the theory of Chebyshev approximations for analytic functions is presented to construct efficient grids for validating solutions of boundary value problems. The effectiveness of the proposed method is demonstrated by validating long periodic and connecting orbits in the Lorenz system for which validation without domain decomposition is not feasible.</p>

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36

Li, Yang, Wanchun Chen, and Liang Yang. "Linear Pseudospectral Method with Chebyshev Collocation for Optimal Control Problems with Unspecified Terminal Time." Aerospace 9, no. 8 (August 20, 2022): 458. http://dx.doi.org/10.3390/aerospace9080458.

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In this paper, a linear Chebyshev pseudospectral method (LCPM) is proposed to solve the nonlinear optimal control problems (OCPs) with hard terminal constraints and unspecified final time, which uses Chebyshev collocation scheme and quasi-linearization. First, Taylor expansion around the nonlinear differential equations of the system is used to obtain a set of linear perturbation equations. Second, the first-order necessary conditions for OCPs with these linear equations and unspecified terminal time are derived, which provide the successive correction formulas of control and terminal time. Traditionally, these formulas are linear time varying and cannot be solved in an analytical manner. Third, Lagrange interpolation, whose supporting points are orthogonal Chebyshev–Gauss–Lobatto (CGL), is employed to discretize the resulting problem. Therefore, a series of analytical correction formulas are successfully derived in approximating polynomial space. It should be noted that Chebyshev approximation is close to the best polynomial approximation, and CGL points can be solved in closed form. Finally, LCPM is applied to the air-to-ground missile guidance problem. The simulation results show that it has high computational efficiency and convergence rate. A comparison with the other typical OCP solvers is provided to verify the optimality of the proposed algorithm. In addition, the results of Monte Carlo simulations are presented, which show that the proposed algorithm has strong robustness and stability. Therefore, the proposed method has potential to be onboard application.

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37

Guariglia, Emanuel, and Rodrigo Capobianco Guido. "Chebyshev Wavelet Analysis." Journal of Function Spaces 2022 (June 30, 2022): 1–17. http://dx.doi.org/10.1155/2022/5542054.

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This paper deals with Chebyshev wavelets. We analyze their properties computing their Fourier transform. Moreover, we discuss the differential properties of Chebyshev wavelets due to the connection coefficients. Uniform convergence of Chebyshev wavelets and their approximation error allow us to provide rigorous proofs. In particular, we expand the mother wavelet in Taylor series with an application both in fractional calculus and fractal geometry. Finally, we give two examples concerning the main properties proved.

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38

Rababah, Abedallah M. "The best quintic Chebyshev approximation of circular arcs of order ten." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 5 (October 1, 2019): 3779. http://dx.doi.org/10.11591/ijece.v9i5.pp3779-3785.

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<p>Mathematically, circles are represented by trigonometric parametric equations and implicit equations. Both forms are not proper for computer applications and CAD systems. In this paper, a quintic polynomial approximation for a circular arc is presented. This approximation is set so that the error function is of degree $10$ rather than $6$; the Chebyshev error function equioscillates $11$ times rather than $7$; the approximation order is $10$ rather than $6$. The method approximates more than the full circle with Chebyshev uniform error of $1/2^{9}$. The examples show the competence and simplicity of the proposed approximation, and that it can not be improved.</p>

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39

Salas, Alvaro H. S., Gilder-Cieza Altamirano, and Manuel Sánchez-Chero. "Solution to a Damped Duffing Equation Using He’s Frequency Approach." Scientific World Journal 2022 (July 11, 2022): 1–10. http://dx.doi.org/10.1155/2022/5009722.

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In this paper, we generalize He’s frequency approach for solving the damped Duffing equation by introducing a time varying amplitude. We also solve this equation by means of the homotopy method and the Lindstedt–Poincaré method. High accurate formulas for approximating the Jacobi elliptic function cn are formally derived using Chebyshev and Pade approximation techniques.

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40

Vlček, Miroslav. "CHEBYSHEV POLYNOMIAL APPROXIMATION FOR ACTIVATION SIGMOID FUNCTION." Neural Network World 22, no. 4 (2012): 387–93. http://dx.doi.org/10.14311/nnw.2012.22.023.

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41

Chit, N. N., and J. S. Mason. "Complex Chebyshev approximation for FIR digital filters." IEEE Transactions on Signal Processing 39, no. 1 (1991): 49–54. http://dx.doi.org/10.1109/78.80764.

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42

Karam, L. J., and J. H. McClellan. "Complex Chebyshev approximation for FIR filter design." IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 42, no. 3 (March 1995): 207–16. http://dx.doi.org/10.1109/82.372870.

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43

Kro{ó, Andr{ás. "Chebyshev rank in $L\sb 1$-approximation." Transactions of the American Mathematical Society 296, no. 1 (January 1, 1986): 301. http://dx.doi.org/10.1090/s0002-9947-1986-0837813-5.

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44

Cuenya, Héctor Hugo, and Fabián Eduardo Levis. "Nonlinear Chebyshev approximation to set-valued functions." Optimization 65, no. 8 (March 23, 2016): 1519–29. http://dx.doi.org/10.1080/02331934.2016.1163554.

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45

Abril-Raymundo, M. R., and B. Garcı́a-Archilla. "Approximation properties of a mapped Chebyshev method." Applied Numerical Mathematics 32, no. 2 (February 2000): 119–36. http://dx.doi.org/10.1016/s0168-9274(99)00017-3.

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46

Bartelt, Martin, Edwin H. Kaufman, and John Swetits. "Uniform Lipschitz constants in Chebyshev polynomial approximation." Journal of Approximation Theory 62, no. 1 (July 1990): 23–38. http://dx.doi.org/10.1016/0021-9045(90)90044-q.

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Drieschner, Rudolf. "Chebyshev approximation to data by geometric elements." Numerical Algorithms 5, no. 10 (October 1993): 509–22. http://dx.doi.org/10.1007/bf02108666.

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Malachivskyy, P. S., Ya V. Pizyur, R. P. Malachivskyi, and O. M. Ukhanska. "Chebyshev Approximation of Functions of Several Variables." Cybernetics and Systems Analysis 56, no. 1 (January 2020): 118–25. http://dx.doi.org/10.1007/s10559-020-00227-8.

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Shuman, David I., Pierre Vandergheynst, Daniel Kressner, and Pascal Frossard. "Distributed Signal Processing via Chebyshev Polynomial Approximation." IEEE Transactions on Signal and Information Processing over Networks 4, no. 4 (December 2018): 736–51. http://dx.doi.org/10.1109/tsipn.2018.2824239.

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Eisele, E. F. "Chebyshev Approximation of Plane Curves by Splines." Journal of Approximation Theory 76, no. 2 (February 1994): 133–48. http://dx.doi.org/10.1006/jath.1994.1010.

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