Parallel implementations for solving generalized eigenvalue problems with symmetric sparse matrices
type: Item
instance of: scholarly article
title: Parallel implementations for solving generalized eigenvalue problems with symmetric sparse matrices
zbMATH Open document ID: 0782.65058
DOI: 10.1016/0168-9274(93)90100-6
author: Bernard Philippe
author: Brigitte Vital
published in: Applied Numerical Mathematics
publication date: 1993-10-06T00:00:00Z
review text: The authors consider the solution of the generalized eigenvalue problem \(Ax = \lambda Mx\), where \(A\) and \(M\) are real symmetric matrices and \(M\) is positive definite. They compare numerically three algorithms: Reduction to a standard eigenvalue problem, multisectioning with Sturm sequences, and the Lanczos method. In the first algorithm the use of one vector processor for an effective Givens transformation is discussed. Parallel implementations for the following two algorithms are considered. All the tests are performed on matrices which belong to the Harwell- Boeing set of test matrices.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 425890
zbMATH Keywords: symmetric sparse matrices
zbMATH Keywords: generalized eigenvalue problem
zbMATH Keywords: Reduction
zbMATH Keywords: multisectioning
zbMATH Keywords: Lanczos method
zbMATH Keywords: algorithm
zbMATH Keywords: Givens transformation
zbMATH Keywords: Parallel implementations
zbMATH Keywords: Harwell-Boeing set of test matrices
reviewed by: Jan Zítko
describes a project that uses: zeroin
MaRDI profile type: Publication
full work available at URL: 0168-9274(93)90100-6
OpenAlex ID: W2019610696
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description: scientific article; zbMATH DE number 425890