On expansions in orthogonal polynomials
type: Item
instance of: scholarly article
title: On expansions in orthogonal polynomials
zbMATH Open document ID: 1277.42029
published in: Advances in Computational Mathematics
publication date: 2013-04-15T00:00:00Z
review text: In 2011, \textit{A. Iserles} [Numer. Math. 117, No. 3, 529--553 (2011; Zbl 1211.33001)] introduced an \(\mathcal{O}(N \log N)\) algorithm for the computation of the first \(N\) coefficients in an expansion of an analytic function in Legendre polynomials. The same year, the authors extended the underlying framework to expansions in ultraspherical polynomials. These approaches rest upon three steps. In the paper under review, the authors demonstrate that the first two steps remain valid for a large variety of orthogonal systems.
reviewed by: Kenier Castillo
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 30E05
zbMATH DE Number: 6153870
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: fast expansions
zbMATH Keywords: Jacobi matrix
zbMATH Keywords: hypergeometric functions
author: María-José Cantero
author: Arieh Iserles
MaRDI profile type: Publication
full work available at URL: s10444-011-9225-0
OpenAlex ID: W2026457621
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DOI: 10.1007/S10444-011-9225-0
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description: scientific article; zbMATH DE number 6153870