Tau-method approximations for the Bessel function \(Y_ 1 (z)\)
type: Item
instance of: scholarly article
title: Tau-method approximations for the Bessel function \(Y_ 1 (z)\)
zbMATH Open document ID: 0834.65005
DOI: 10.1016/0898-1221(95)00121-E
author: Jun Zhang
publication date: 1996-03-31T00:00:00Z
review text: The paper deals with an application of the Lanczos \(\tau\)-method in approximating the Bessel function \(Y_1(z)\) of the second kind of order one. Polynomial approximants of \(Y_1(z)\) are obtained from the Bessel differential equation after being perturbed by adding a Faber polynomial term. Maximum and minimum errors in computing \(Y_1(z)\) are listed in a table, where Chebyshev, direct and integrated \(\tau\)-methods can be compared. The present article and a related one by the author and \textit{J. A. Belward} [ibid. 30, No. 7, 5-14 (1995; reviewed above)] -- the latter contains results on the polynomial approximation of the Bessel function \(Y_0(z)\) -- make it possible to compute function values for \(Y_n(z)\), \(n > 1\), using known recurrence relations.
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65A05
Mathematics Subject Classification ID: 34B30
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 811384
zbMATH Keywords: polynomial approximation
zbMATH Keywords: error bounds
zbMATH Keywords: Lanczos tau-method
zbMATH Keywords: Bessel function
zbMATH Keywords: Bessel differential equation
zbMATH Keywords: Faber polynomial
zbMATH Keywords: table
reviewed by: J. Illán
MaRDI profile type: Publication
cites work: Tau-method approximations for the Bessel function \(Y_ 0 (z)\)
cites work: Q5518575
cites work: The Faber Polynomials for Circular Sectors
cites work: The Lanczos Tau-method
cites work: Faber Polynomials and the Faber Series
cites work: Polynomial approximations in the complex plane
full work available at URL: 0898-1221(95)00121-e
OpenAlex ID: W2988925967
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 811384