Methods for computing lower bounds to eigenvalues of self-adjoint operators
type: Item
instance of: scholarly article
title: Methods for computing lower bounds to eigenvalues of self-adjoint operators
zbMATH Open document ID: 0857.65063
author: Friedrich Goerisch
author: Christopher Beattie
published in: Numerische Mathematik
publication date: 1997-03-16T00:00:00Z
review text: The authors describe a new approach for computing lower bounds on eigenvalues of selfadjoint operators (in particular differential operators). The derivation of the method depends on intermediate problem formulation but needs no information on eigenvectors of the base problem. The proposed method permits effective use of finite element trial functions; this yields a computational method which involves sparse well-structured matrices. This method may be coupled with a Rayleigh-Ritz method (for computing upper bounds) to obtain bounds on eigenvalues as is illustrated by two computational examples.
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 47A75
Mathematics Subject Classification ID: 47B25
zbMATH DE Number: 839153
zbMATH Keywords: lower bounds on eigenvalues
zbMATH Keywords: selfadjoint operators
zbMATH Keywords: differential operators
zbMATH Keywords: finite element
zbMATH Keywords: Rayleigh-Ritz method
zbMATH Keywords: upper bounds
zbMATH Keywords: computational examples
reviewed by: A. J. Meir
MaRDI profile type: Publication
full work available at URL: s002110050164
OpenAlex ID: W2039976375
DOI: 10.1007/S002110050164
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description: scientific article; zbMATH DE number 839153