Results 21 to 30 of about 3,011 (212)
Jacobi Polynomials on the Bernstein Ellipse [PDF]
Journal of Scientific Computing, 2017 In this paper, we are concerned with Jacobi polynomials $P_n^{(α,β)}(x)$ on the Bernstein ellipse with motivation mainly coming from recent studies of convergence rate of spectral interpolation. An explicit representation of $P_n^{(α,β)}(x)$ is derived in the variable of parametrization. This formula further allows us to show that the maximum value of $
Haiyong Wang, Lun Zhang
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Mathematics, 2023 The purpose of this article is to give relations among the uniform B-splines, the Bernstein basis functions, and certain families of special numbers and polynomials with the aid of the generating functions method.
Yilmaz Simsek
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Use of Bernstein Polynomial in Numerical Solution of Nonlinear Fred Holm Integral Equation [PDF]
Engineering and Technology Journal, 2011 In this paper, Bernstein polynomials with different degree has been used to approximate the solution of nonlinear Fredholm integral equations. A comparison between the different degree of Bernstein polynomials has been made depending on absolute error ...
Khawla A .AL-Zubaidy, Muna M. Mustafa
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A New Generating Function of (q-) Bernstein-Type Polynomials and Their Interpolation Function
Abstract and Applied Analysis, 2010 The main object of this paper is to construct a new generating function of the (q-) Bernstein-type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and derivative of the (q-
Yilmaz Simsek, Mehmet Acikgoz
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Sparse polynomial interpolation with Bernstein polynomials
TURKISH JOURNAL OF MATHEMATICS, 2021 Summary: We present an algorithm for interpolating an unknown univariate polynomial \(f\) that has a \(t\) sparse representation (\(t\ll\deg(f)\)) using Bernstein polynomials as term basis from \(2t\) evaluations. Our method is based on manipulating given black box polynomial for \(f\) so that we can make use of Prony's algorithm.
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Some identities of degenerate Euler polynomials associated with degenerate Bernstein polynomials
Journal of Inequalities and Applications, 2019 In this paper, we investigate some properties and identities for degenerate Euler polynomials in connection with degenerate Bernstein polynomials by means of fermionic p-adic integrals on Zp $\mathbb{Z}_{p}$ and generating functions.
Won Joo Kim +3 more
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Schur-Type Inequalities for Complex Polynomials with no Zeros in the Unit Disk
Journal of Inequalities and Applications, 2007 Starting out from a question posed by T. Erdélyi and J. Szabados, we consider Schur-type inequalities for the classes of complex algebraic polynomials having no zeros within the unit disk D.
Szilárd Gy. Révész
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Shape Preserving Properties for q-Bernstein-Stancu Operators
Journal of Mathematics, 2014 We investigate shape preserving for q-Bernstein-Stancu polynomials Bnq,α(f;x) introduced by Nowak in 2009. When α=0, Bnq,α(f;x) reduces to the well-known q-Bernstein polynomials introduced by Phillips in 1997; when q=1, Bnq,α(f;x) reduces to Bernstein ...
Yali Wang, Yinying Zhou
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Mathematics, 2022 An alternative approach, known today as the Bernstein polynomials, to the Weierstrass uniform approximation theorem was provided by Bernstein. These basis polynomials have attained increasing momentum, especially in operator theory, integral equations ...
Faruk Özger +2 more
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The Trigonometric Polynomial Like Bernstein Polynomial [PDF]
The Scientific World Journal, 2014 A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent.
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