A note on the tau-method approximations for the Bessel functions \(Y_ 0(z)\) and \(Y_ 1(z)\)
type: Item
instance of: scholarly article
title: A note on the tau-method approximations for the Bessel functions \(Y_ 0(z)\) and \(Y_ 1(z)\)
zbMATH Open document ID: 0858.65013
DOI: 10.1016/0898-1221(96)00043-0
author: Jun Zhang
publication date: 1997-03-11T00:00:00Z
review text: This paper completes and improves the previous one by the author and \textit{J. A. Belward} [Comput. Math. Appl. 30, No. 7, 5-14 (1995; Zbl 0834.65004)] and the one by the author [ibid. 30, No. 7, 15-19 (1995; Zbl 0834.65005)], dealing with the application of a particular version of the Lanczos \(\tau\)-methods to approximate the Bessel functions \(Y_0(z)\) and \(Y_1(z)\) in the complex plane. That version uses Faber polynomials up to degree 15 as the perturbation terms. The author introduces symbolic representation of the scaled Faber polynomials and the appropriately modified (automated) \(\tau\)-method. Numerical comparisons, showing the accuracy improvements achieved by this new version of the \(\tau\)-method, are given and discussed.
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 915125
zbMATH Keywords: Lanczos tau method
zbMATH Keywords: numerical examples
zbMATH Keywords: Bessel functions
zbMATH Keywords: Faber polynomials
reviewed by: Luigi Gatteschi
MaRDI profile type: Publication
full work available at URL: 0898-1221(96)00043-0
OpenAlex ID: W1971970383
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 915125