Application of Chebyshev, and Legendre polynomials on discrete point set to function interpolation and solving Fredholm integral equations
type: Item
instance of: scholarly article
title: Application of Chebyshev, and Legendre polynomials on discrete point set to function interpolation and solving Fredholm integral equations
zbMATH Open document ID: 0963.65143
DOI: 10.1016/S0010-4655(99)00520-2
author: I. P. Streltsov
published in: Computer Physics Communications
publication date: 2001-06-19T00:00:00Z
review text: The author proposes to solve Fredholm integral equations of the first and second kind \[ \int_{-1}^1 K(x,y) f(y) dy= q(x), \quad f(x)-\lambda \int_{-1}^1 K(x,y) f(y) dy= q(x), \quad x \in [-1,1] \] by replacing of \(K(x,y), q(x), f(x)\) with their expansions \[ K_n (x,y)=\sum_{k=0}^n \sum_{l=0}^n C_{kl} P_k(x) P_l(y), \quad q_n (x)=\sum_{k=0}^n Q_k P_k (x), \quad f_n (x)=\sum_{k=0}^n e_k P_k(x), \] where \(P_k (x)\) are Chebyshev or Legendre polynomials. Since integral equations of the first kind are ill-posed, the method is not in general correct when applied to such problems.
reviewed by: Mikhail Yu. Kokurin
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 65R30
zbMATH DE Number: 1437197
zbMATH Keywords: orthogonal polynomials on discrete sets
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: Legendre polynomials
zbMATH Keywords: series expansions
zbMATH Keywords: ill-posed problems
zbMATH Keywords: Fredholm integral equations
MaRDI profile type: Publication
full work available at URL: s0010-4655(99)00520-2
OpenAlex ID: W2042952898
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description: scientific article; zbMATH DE number 1437197