On extensions of the power method for normal operators
type: Item
instance of: scholarly article
title: On extensions of the power method for normal operators
zbMATH Open document ID: 0678.65023
DOI: 10.1016/0024-3795(89)90379-0
author: Avram Sidi
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: In a recent work by the author and \textit{J. Bridger} [J.Comput. Appl. Math. 22, 35-61 (1988; Zbl 0646.65030)] some old and some new extensions of the power method have been considered. It has been shown for some of these extensions that they enable one to estimate several dominant eigenvalues of an arbitrary square matrix. This paper continues this analysis for one of these extensions, namely, the minimal polynomial extrapolation (MPE) extension, as it is employed in estimating the dominant eigenvalues of a normal matrix. Section 1 gives a brief description of two versions of the MPE extension of the power method. Section 2 shows that the convergence rate of these methods for normal matrices is twice that for nonnormal matrices. Section 3 suggests deflation-type extensions of the power method for normal matrices and analyzes their convergence.
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 4111900
zbMATH Keywords: minimal polynomial extrapolation extension
zbMATH Keywords: power method
zbMATH Keywords: dominant eigenvalues
zbMATH Keywords: normal matrix
zbMATH Keywords: convergence rate
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90379-0
OpenAlex ID: W1968944404
cites work: Convergence and stability analyses for some vector extrapolation methods in the presence of defective iteration matrices
cites work: Acceleration of Convergence of Vector Sequences
cites work: Q5674306
description: scientific article; zbMATH DE number 4111900