Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation
type: Item
instance of: scholarly article
title: Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation
zbMATH Open document ID: 1063.33028
published in: Constructive Approximation
publication date: 2004-09-22T00:00:00Z
review text: The Rayleigh-Ritz method yields a decreasing sequence \(\mu_r\) that approximates the desired eigenvalue \(\lambda \) of Mathieu function or of spheroidal wave function. The method produces also a sequence of elementary functions \(g\) that approximates the desired eigenfunction \(f\) of the same functions. This paper provides answers to some questions about the rate of convergence \(\mu _r\to \lambda \) and \(g_r \to f\) as \(r\to \infty \), to the error bounds for the maximum norm \(\| g_r -f \| _\infty \) and to other convergence properties of the method. Errors are investigated by interesting numerical experimentations.
Mathematics Subject Classification ID: 33E10
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65L70
zbMATH DE Number: 2101899
zbMATH Keywords: Rayleigh-Ritz method
zbMATH Keywords: Mathieu equation
zbMATH Keywords: Spheroidal wave equation
zbMATH Keywords: tridiagonal matrix
zbMATH Keywords: error estimates.
author: Hans W. Volkmer
reviewed by: Luigi Gatteschi
describes a project that uses: MTIEU1
MaRDI profile type: Publication
full work available at URL: s00365-002-0527-9
OpenAlex ID: W2056517747
DOI: 10.1007/S00365-002-0527-9
description: scientific article; zbMATH DE number 2101899