A theoretical comparison between inner products in the shift-invert Arnoldi method and the spectral transformation Lanczos method
type: Item
instance of: scholarly article
title: A theoretical comparison between inner products in the shift-invert Arnoldi method and the spectral transformation Lanczos method
zbMATH Open document ID: 0915.65027
author: Karl Meerbergen
publication date: 1999-02-08T00:00:00Z
full work available at URL: https://eudml.org/doc/119805
full work available at URL: vol.7.1998
review text: This paper is concerned with the solution of generalized eigenvalue problems of the form: \[ Ax= \lambda Bx,\quad A,B\in \mathbb{R}^{n\times n},\quad x\neq 0, \] where \(A\) may be symmetric or non-symmetric, and \(B\) is symmetric positive (semi)definite, by the spectral transformation Lanczos method and the shift-invert Arnoldi method. The theory is illustrated by numerical examples arising from acoustic and structural finite element models. The theoretical results are extended to the Navier-Stokes problem.
reviewed by: Costică Moroşanu
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 1249447
zbMATH Keywords: shift-invert Arnoldi method
zbMATH Keywords: spectral transformation Lanczos method
zbMATH Keywords: generalized eigenvalue problem
zbMATH Keywords: numerical examples
zbMATH Keywords: finite element models
zbMATH Keywords: Navier-Stokes problem
MaRDI profile type: Publication
published in: ETNA - Electronic Transactions on Numerical Analysis
description: scientific article; zbMATH DE number 1249447