A parallel processed scheme for the eigenproblem of positive definite matrices
type: Item
instance of: scholarly article
title: A parallel processed scheme for the eigenproblem of positive definite matrices
zbMATH Open document ID: 0823.65039
DOI: 10.1016/0377-0427(94)90397-2
published in: Journal of Computational and Applied Mathematics
publication date: 1995-04-02T00:00:00Z
review text: The largest eigenvalue of a symmetric matrix is computed by a Jacobi type algorithm that in each iteration zeroes out the first column with a Householder reflection from the left. Application from the right fills the zeros again, but the norm of the first column will tend to zero with a rate comparable to the power method. Similar methods have been proposed from time to time, see e.g. \textit{C. D. LaBudde} [Math. Comput. 18, 118-123 (1964; Zbl 0115.344)] or \textit{A. Ruhe} [BIT 20, 88-96 (1980; Zbl 0435.65029)].
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 739574
zbMATH Keywords: parallel computation
zbMATH Keywords: largest eigenvalue
zbMATH Keywords: symmetric matrix
zbMATH Keywords: Jacobi type algorithm
zbMATH Keywords: Householder reflection
zbMATH Keywords: power method
author: Mohamed Ahmed Shalaby
reviewed by: Axel Ruhe
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)90397-2
OpenAlex ID: W1985350772
cites work: Ordinary Differential Equations and the Symmetric Eigenvalue Problem
cites work: Eigenvalues of tridiagonal matrices: An alternative to Givens' method
cites work: A new look at the Lanczos algorithm for solving symmetric systems of linear equations
description: scientific article; zbMATH DE number 739574