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Journal articles on the topic 'Chebyshev approximation'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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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

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2

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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3

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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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 present

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5

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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6

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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7

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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8

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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9

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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10

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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11

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

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12

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

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13

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

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14

Zhuhua, Luo. "Generalized simultaneous Chebyshev approximation." Approximation Theory and its Applications 8, no. 1 (1992): 87–96. http://dx.doi.org/10.1007/bf02907595.

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15

Niu, Cuixia, Huiqing Liao, Heping Ma, and Hua Wu. "Approximation Properties of Chebyshev Polynomials in the Legendre Norm." Mathematics 9, no. 24 (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 sampli

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16

Potseiko, P. G., and E. Rovba. "Vallée Poussin sums of rational Fourier–Chebyshev integral operators and approximations of the Markov function." St. Petersburg Mathematical Journal 35, no. 5 (2024): 879–96. https://doi.org/10.1090/spmj/1834.

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Rational approximations of the Markov function on the segment [ − 1 , 1 ] [-1,1] are studied. The Vallée Poussin sums of rational integral Fourier–Chebyshev operators as an approximation apparatus with a fixed number of geometrically distinct poles are chosen. For the constructed rational approximation method, integral representations of approximations and upper estimates of uniform approximations are established. For the Markov function with a measure whose derivative is a function that has a power-law singularity on the segment [ − 1 , 1 ] [-1, 1] , upper estimates of pointwise and uniform a

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17

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 C

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18

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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19

Langhammer, Lukas, Roman Sotner, and Radek Theumer. "Various-Order Low-Pass Filter with the Electronic Change of Its Approximation." Sensors 23, no. 19 (2023): 8057. http://dx.doi.org/10.3390/s23198057.

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The design of a low-pass-frequency filter with the electronic change of the approximation characteristics of resulting responses is presented. The filter also offers the reconnection-less reconfiguration of the order (1st-, 2nd-, 3rd- and 4th-order functions are available). Furthermore, the filter offers the electronic control of the cut-off frequency of the output response. The feature of the electronic change in the approximation characteristics is investigated for the Butterworth, Bessel, Elliptic, Chebyshev and Inverse Chebyshev approximations. The design is verified by PSpice simulations

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20

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 (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

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21

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 (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 repr

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22

Kowynia, Joanna. "The unicity of best approximation in a space of compact operators." MATHEMATICA SCANDINAVICA 108, no. 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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23

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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24

Malachivskyy, P. S., L. S. Melnychok, and Ya V. Pizyur. "Chebyshev Approximation by Gompertz Function." Journal of Mathematical Sciences 287, no. 2 (2025): 216–22. https://doi.org/10.1007/s10958-025-07586-7.

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25

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

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26

Alsharif, Faisal. "Quasi-Interpolation on Chebyshev Grids with Boundary Corrections." Computation 12, no. 5 (2024): 100. http://dx.doi.org/10.3390/computation12050100.

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Quasi-interpolation is a powerful tool for approximating functions using radial basis functions (RBFs) such as Gaussian kernels. This avoids solving large systems of equations as in RBF interpolation. However, quasi-interpolation with Gaussian kernels on compact intervals can have significant errors near the boundaries. This paper proposes a quasi-interpolation method with Gaussian kernels using Chebyshev points and boundary corrections to improve the approximation near the boundaries. The boundary corrections use a linear approximation of the function beyond the interval to estimate the trunc

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27

Malachivskyi, R. P., R. A. Bun, and I. P. Medynskyi. "Chebyshev approximation by the exponent from a rational expression." Mathematical Modeling and Computing 12, no. 1 (2025): 233–40. https://doi.org/10.23939/mmc2025.01.233.

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A method for constructing Chebyshev approximation with relative error of the exponential from a rational expression is proposed. It implies constructing an intermediate Chebyshev approximation with absolute error by a rational expression of the logarithm of the function being approximated. The approximation by a rational expression is calculated as the boundary mean-power approximation using an iterative scheme based on the least squares method with two variable weight functions. The presented results of solving test examples confirm the fast convergence of the method.

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28

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 Ch

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29

Journal, Baghdad Science. "Orthogonal Functions Solving Linear functional Differential EquationsUsing Chebyshev Polynomial." Baghdad Science Journal 5, no. 1 (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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30

Mizel, Abdul Khaliqe Ewaid. "Orthogonal Functions Solving Linear functional Differential EquationsUsing Chebyshev Polynomial." Baghdad Science Journal 5, no. 1 (2008): 143–48. http://dx.doi.org/10.21123/bsj.2008.5.1.143-148.

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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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31

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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32

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 (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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33

Ganesan, Timothy. "An Approximation of the Prime Counting Function and a New Representation of the Riemann Zeta Function." Mathematics 12, no. 17 (2024): 2624. http://dx.doi.org/10.3390/math12172624.

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Determining the exact number of primes at large magnitudes is computationally intensive, making approximation methods (e.g., the logarithmic integral, prime number theorem, Riemann zeta function, Chebyshev’s estimates, etc.) particularly valuable. These methods also offer avenues for number-theoretic exploration through analytical manipulation. In this work, we introduce a novel approximation function, ϕ(n), which adds to the existing repertoire of approximation methods and provides a fresh perspective for number-theoretic studies. Deeper analytical investigation of ϕ(n) reveals modified repre

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34

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 wit

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35

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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36

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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37

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

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38

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

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39

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 (1996): 162–74. http://dx.doi.org/10.1016/s0167-2789(96)00164-9.

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40

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

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41

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

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42

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

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43

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

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44

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

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45

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

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46

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 (2013): 877–81. http://dx.doi.org/10.1007/s10559-013-9577-1.

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47

Li, Jiayun, and Yilin Mo. "Markov Parameter Identification via Chebyshev Approximation." IFAC-PapersOnLine 56, no. 2 (2023): 1686–91. http://dx.doi.org/10.1016/j.ifacol.2023.10.1874.

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48

Kumar, Susheel, Gaurav Kumar Mishra, Sudhir Kumar Mishra, and Shyam Lal. "PSEUDO CHEBYSHEV WAVELETS IN TWO DIMENSIONS AND THEIR APPLICATIONS IN THE THEORY OF APPROXIMATION OF FUNCTIONS BELONGING TO LIPSCHITZ CLASS." South East Asian Journal of Mathematics and Mathematical Sciences 20, no. 02 (2024): 247–68. https://doi.org/10.56827/seajmms.2024.2002.19.

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In 2022, the concept of one-dimensional pseudo Chebyshev wavelets was introduced by the authors. Building upon this research, the present article extends the study to two-dimensional pseudo Chebyshev wavelets. It defines and verifies the two-dimensional pseudo Chebyshev wavelet expansion for a functions of two variables. The paper proposes a novel algorithm utilizing the two-dimensional pseudo Chebyshev wavelet method to address computation problems in approximation theory. To demonstrate the validity and applicability of the results, the methods are illustrated through an example and compared

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49

Hassan, Zainab flaih, Hayder Jasim Yousif, and Jolan Lazim Dheyab. "Best approximation on graphs." Journal of Discrete Mathematical Sciences and Cryptography 28, no. 4-A (2025): 1195–99. https://doi.org/10.47974/jdmsc-2143.

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In this paper we define best approximation on graphs when p≥1. The great Russian mathematician P.L. Chebyshev developed approximation theory. Here we study the best on graphs and the problem of uniqueness approximation.

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50

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 (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 an

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