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Incomplete cyclic reduction of banded and strictly diagonally dominant linear systems
Umeå University, Faculty of Science and Technology, Department of Computing Science. (HPC2N)
Umeå University, Faculty of Science and Technology, Department of Computing Science. (HPC2N, UMIT)
2012 (English)In: PARALLEL PROCESSING AND APPLIED MATHEMATICS, PT I / [ed] Wyrzykowski, R., Springer, 2012, 80-91 p.Conference paper, Published paper (Refereed)
Abstract [en]

The ScaLAPACK library contains a pair of routines for solving banded linear systems which are strictly diagonally dominant by rows. Mathematically, the algorithm is complete block cyclic reduction corresponding to a particular block partitioning of the system. In this paper we extend Heller’s analysis of incomplete cyclic reduction for block tridiagonal systems to the ScaLAPACK case. We obtain a tight estimate on the significance of the off diagonal blocks of the tridiagonal linear systems generated by the cyclic reduction algorithm. Numerical experiments illustrate the advantage of omitting all but the first reduction step for a class of matrices related to high order approximations of the Laplace operator.

Place, publisher, year, edition, pages
Springer, 2012. 80-91 p.
Series
Lecture Notes in Computer Science, ISSN 0302-9743 ; 7203
Keyword [en]
Banded or block tridiagonal linear systems, strict diagonal dominance, incomplete cyclic reduction, ScaLAPACK
National Category
Computer Science
Research subject
Computing Science
Identifiers
URN: urn:nbn:se:umu:diva-50786DOI: 10.1007/978-3-642-31464-3_9ISI: 000313192800009ISBN: 978-3-642-31463-6 (print)OAI: oai:DiVA.org:umu-50786DiVA: diva2:468793
Conference
9th International Conference on Parallel Processing and Applied Mathematics, SEP 11-14, 2011, Torun, POLAND
Available from: 2012-02-20 Created: 2011-12-21 Last updated: 2017-01-16Bibliographically approved

Open Access in DiVA

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