An analysis of the Rayleigh-Ritz method for approximating eigenspaces
type: Item
instance of: scholarly article
zbMATH Open document ID: 0968.65020
DOI: 10.1090/S0025-5718-00-01208-4
author: Zhongxiao Jia
author: G. W. Stewart
published in: Mathematics of Computation
publication date: 2001-02-19T00:00:00Z
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 1566123
zbMATH Keywords: Rayleigh-Ritz method
zbMATH Keywords: Ritz vectors
zbMATH Keywords: eigenspace
zbMATH Keywords: eigenvalues
zbMATH Keywords: convergence
describes a project that uses: JDQZ
MaRDI profile type: Publication
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title: An analysis of the Rayleigh-Ritz method for approximating eigenspaces
review text: This paper concerns the computation of approximations to an eigenspace \({\mathcal X}\) of a general matrix \(A\) without the assumptions that the eigenvalues of \(A\) are distinct or that \(A\) is diagonalizable. Using a subspace \({\mathcal W}\) containing an approximation to \({\mathcal X}\), the method produces Ritz pairs \((N,\widetilde X)\) approximating \((L,X)\), \(X\) a basis of \({\mathcal X}\). Under a ``uniform separation condition'' and with uniform adjustment it converges linearly as the sine and the angle between \({\mathcal X}\) and \({\mathcal W}\) approaches zero (and without that condition when \(\dim{\mathcal X}=1\)). Alternatively, convergence without that condition is obtained for ``refined Ritz vectors''.
reviewed by: Erwin O. Kreyszig
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description: scientific article