A Chebyshev polynomial interval-searching method (``Lanczos economization'') for solving a nonlinear equation with application to the nonlinear eigenvalue problem
type: Item
instance of: scholarly article
title: A Chebyshev polynomial interval-searching method (``Lanczos economization'') for solving a nonlinear equation with application to the nonlinear eigenvalue problem
zbMATH Open document ID: 0823.65047
published in: Journal of Computational Physics
publication date: 1995-10-24T00:00:00Z
review text: Assume that we want to compute some zeros of a function \(f\) and that the evaluation of \(f(x)\) for a given value of \(x\) is expensive. In this case it may be better to first compute zeros of a polynomial approximation \(f_ N\) than to apply Newton's method directly. This is elucidated for the computation of eigenvalues via zeros of determinants. \{Reviewer's remark: The computation of eigenvalues via the characteristic polynomial can be recommended only in some well-known special cases.\}.
reviewed by: D. Braess
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 65H17
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 26C10
zbMATH DE Number: 758610
zbMATH Keywords: Chebyshev polynomial interval-searching method
zbMATH Keywords: Lanczos economization
zbMATH Keywords: nonlinear eigenvalue problem
zbMATH Keywords: approximation of zeros
zbMATH Keywords: polynomial approximation
zbMATH Keywords: Newton's method
zbMATH Keywords: eigenvalues
zbMATH Keywords: zeros of determinants
author: John P. Boyd
MaRDI profile type: Publication
full work available at URL: jcph.1995.1075
OpenAlex ID: W2003704367
DOI: 10.1006/JCPH.1995.1075
description: scientific article; zbMATH DE number 758610