Parallel algorithm for solving some spectral problems of linear algebra
type: Item
instance of: scholarly article
title: Parallel algorithm for solving some spectral problems of linear algebra
zbMATH Open document ID: 0782.65056
DOI: 10.1016/0024-3795(93)90477-6
author: A. Malyshev
published in: Linear Algebra and its Applications
publication date: 1993-08-25T00:00:00Z
review text: An algorithm for the computation of the projection matrices \(P\) and \((I- P)\) onto the deflating subspaces of matrix pencils corresponding to the eigenvalues inside and outside the unit circle is described. Furthermore, the convergence of this algorithm and its implementation on parallel computers with shared memory are discussed.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 15A22
zbMATH DE Number: 398930
zbMATH Keywords: projection matrices
zbMATH Keywords: deflating subspaces
zbMATH Keywords: matrix pencils
zbMATH Keywords: eigenvalues
zbMATH Keywords: convergence
zbMATH Keywords: algorithm
zbMATH Keywords: parallel computers
reviewed by: Michael Jung
describes a project that uses: LAPACK
MaRDI profile type: Publication
full work available at URL: 0024-3795(93)90477-6
OpenAlex ID: W1979674329
cites work: An improved algorithm for the computation of Kronecker's canonical form of a singular pencil
cites work: The WY Representation for Products of Householder Matrices
cites work: An effectively calculable parameter for the stability property of a system of linear differential equations with constant coefficients
cites work: An estimate of the Green matrix and the continuity of the dichotomy parameter
cites work: Circular dichotomy of the matrix spectrum
cites work: Computing stable eigendecompositions of matrices
cites work: Computing stable eigendecompositions of matrix pencils
cites work: Problem of the dichotomy of the spectrum of a matrix
cites work: Q3221817
cites work: AB-algorithm and its modifications for the spectral problems of linear pencils of matrices
cites work: Q4401802
cites work: Computing invariant subspaces of a regular linear pencil of matrices
cites work: On solution of large systems of linear equations with block-Toeplitz banded matrices
cites work: Q3996786
cites work: Guaranteed accuracy in spectral problems of linear algebra. II
cites work: Nineteen Dubious Ways to Compute the Exponential of a Matrix
cites work: An Algorithm for Generalized Matrix Eigenvalue Problems
cites work: A Storage-Efficient $WY$ Representation for Products of Householder Transformations
cites work: On the Sensitivity of the Eigenvalue Problem $Ax = \lambda Bx$
cites work: Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
cites work: The computation of Kronecker's canonical form of a singular pencil
cites work: A Generalized Eigenvalue Approach for Solving Riccati Equations
cites work: Q3666140
cites work: Computing integrals involving the matrix exponential
cites work: Q5674306
description: scientific article; zbMATH DE number 398930