Block reduction of matrices to condensed forms for eigenvalue computations
type: Item
instance of: scholarly article
title: Block reduction of matrices to condensed forms for eigenvalue computations
zbMATH Open document ID: 0679.65025
DOI: 10.1016/0377-0427(89)90367-1
author: Jack Dongarra
author: Danny C. Sorensen
author: S. Hammarling
published in: Journal of Computational and Applied Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The authors describe block algorithms for the reduction of a (real) symmetric matrix to a tridiagonal form and that of a general matrix to a bidiagonal form by using Householder transformations. The same approach can be used in the reduction to Hessenberg form. These reductions to condensed forms comprise a preliminary step in the computation of eigenvalues or singular values. The authors also show how these reductions may be pipelined with the divide and conquer technique for computing the eigensystem of a symmetric matrix or the singular value decomposition of a general matrix. These considerations have significant performance advantages on parallel-vector processors.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 4113854
zbMATH Keywords: reduction to tridiagonal form
zbMATH Keywords: block algorithms
zbMATH Keywords: Householder transformations
zbMATH Keywords: reduction to Hessenberg form
zbMATH Keywords: reductions to condensed forms
zbMATH Keywords: eigenvalues
zbMATH Keywords: divide and conquer technique
zbMATH Keywords: singular value decomposition
zbMATH Keywords: parallel-vector processors
reviewed by: Ferenc Móricz
describes a project that uses: BLAS
MaRDI profile type: Publication
full work available at URL: 0377-0427(89)90367-1
OpenAlex ID: W2164895445
cites work: The WY Representation for Products of Householder Matrices
cites work: A set of level 3 basic linear algebra subprograms
cites work: Implementing Dense Linear Algebra Algorithms Using Multitasking on the CRAY X-MP-4 (or Approaching the Gigaflop)
cites work: Squeezing the most out of eigenvalue solvers on high-performance computers
cites work: Linear algebra on high performance computers
cites work: A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem
cites work: Analysis of Algorithms for Reflections in Bisectors
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description: scientific article; zbMATH DE number 4113854