Parallel implementation of bisection for the calculation of eigenvalues of tridiagonal symmetric matrices
type: Item
instance of: scholarly article
title: Parallel implementation of bisection for the calculation of eigenvalues of tridiagonal symmetric matrices
zbMATH Open document ID: 0584.65014
DOI: 10.1007/BF02252736
author: Herbert J. Bernstein
author: Max Goldstein
published in: Computing
publication date: 1986-01-01T00:00:00Z
review text: \textit{D. J. Kuck} and \textit{A. H. Sameh} [Inform. Processing 71, Proc. IFIP Congr. 1971, Ljubljana, Yugoslavia 1971, 1266-1272 (1972; Zbl 0256.65024)], \textit{H.-M. Huang} [A parallel algorithm for symmetric tridiagonal eigenvalue problems. CAC Document No.109, Center for Advanced Computation, University of Illinois at Urbana-Champaign, February 1974] and \textit{Y. Wallach} [Alternating sequential/parallel processing, Lect. Notes in Computer Science 127 (1982; Zbl 0495.68002)] have investigated parallel implementations of Givens' bisection algorithm. On an MIMD (multiple instruction stream - multiple data stream) machine one could apply parallelism on any or all of three levels: within each Sturm sequence calculation, within each individual bisection, or on the outer level assigning intervals to be searched. We show that allocating bisections to individual processors on the outer level is more effective than having processors share the work of a bisection when the number of processors is smaller than the number of eigenvalues to be found.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 68W99
Mathematics Subject Classification ID: 68Q25
zbMATH DE Number: 3936373
zbMATH Keywords: eigenvalue
zbMATH Keywords: parallel algorithm
zbMATH Keywords: tridiagonal symmetric matrices
zbMATH Keywords: parallel implementations
zbMATH Keywords: Givens' bisection algorithm
zbMATH Keywords: MIMD
zbMATH Keywords: multiple instruction stream - multiple data stream
zbMATH Keywords: Sturm sequence
MaRDI profile type: Publication
cites work: Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisection
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cites work: Q5822724
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cites work: Alternating sequential/parallel processing
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full work available at URL: https://doi.org/10.1007/bf02252736
OpenAlex ID: W52224625
description: scientific article; zbMATH DE number 3936373