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Parallel Robust Computation of Generalized Eigenvectors of Matrix Pencils
Umeå University, Faculty of Science and Technology, Department of Computing Science.ORCID iD: 0000-0002-9158-1941
Umeå University, Faculty of Science and Technology, Department of Computing Science.ORCID iD: 0000-0002-3689-0899
2020 (English)In: Parallel Processing and Applied Mathematics: Revised Selected Papers, Part I / [ed] Roman Wyrzykowski, Ewa Deelman, Jack Dongarra, Konrad Karczewski, Springer, 2020, p. 58-69Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we consider the problem of computing generalized eigenvectors of a matrix pencil in real Schur form. In exact arithmetic, this problem can be solved using substitution. In practice, substitution is vulnerable to floating-point overflow. The robust solvers xtgevc in LAPACK prevent overflow by dynamically scaling the eigenvectors.These subroutines are scalar and sequential codes which compute theeigenvectors one by one. In this paper, we discuss how to derive robust algorithms which are blocked and parallel. The new StarNEig librarycontains a robust task-parallel solver Zazamoukh which runs on top of StarPU. Our numerical experiments show that Zazamoukh achieves a super-linear speedup compared with dtgevc for sufficiently large matrices.

Place, publisher, year, edition, pages
Springer, 2020. p. 58-69
Series
Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 12043
Keywords [en]
Generalized eigenvectors, overflow protection, task-parallelism
National Category
Computer Sciences
Research subject
Computer Science; Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-168416DOI: 10.1007/978-3-030-43229-4_6Scopus ID: 2-s2.0-85083956421ISBN: 978-3-030-43228-7 (print)ISBN: 978-3-030-43229-4 (print)OAI: oai:DiVA.org:umu-168416DiVA, id: diva2:1396094
Conference
13th International Conference on Parallel Processing and Applied Mathematics, PPAM 2019, Bialystok, Poland, September 8-11, 2019
Projects
NLAFETAvailable from: 2020-02-25 Created: 2020-02-25 Last updated: 2023-03-24Bibliographically approved

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Kjelgaard Mikkelsen, Carl ChristianMyllykoski, Mirko

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