Homotopy algorithm for symmetric eigenvalue problems
type: Item
instance of: scholarly article
title: Homotopy algorithm for symmetric eigenvalue problems
zbMATH Open document ID: 0653.65025
DOI: 10.1007/BF01390054
published in: Numerische Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133355
review text: The homotopy method can be used to solve eigenvalue-eigenvector problems. The purpose of this paper is to report the numerical experience of the homotopy method of computing eigenpairs for real symmetric tridiagonal matrices together with a couple of new theoretical results. In practice, it is rarely of any interest to compute all the eigenvalues. The homotopy method, having the order preserving property, can provide any specific eigenvalue without calculating any other eigenvalues. Besides this advantage, we note that the homotopy algorithm is to a large degree a parallel algorithm. Numerical experimentation shows that the homotopy method can be very efficient especially for graded matrices.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 4066221
zbMATH Keywords: eigenvalue
zbMATH Keywords: eigenvector
zbMATH Keywords: homotopy continuation method
zbMATH Keywords: symmetric tridiagonal matrices
zbMATH Keywords: parallel algorithm
zbMATH Keywords: graded matrices
author: Tien-Yien Li
author: N. H. Rhee
describes a project that uses: PITCON
describes a project that uses: EISPACK
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4066221