Stability of a pivoting strategy for parallel Gaussian elimination

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3 Scopus citations

Abstract

Gaussian elimination with partial pivoting achieved by adding the pivot row to the kth row at step k, was introduced by Onaga and Takechi in 1986 as a means for reducing communications in parallel implementations. In this paper it is shown that the growth factor of this partial pivoting algorithm is bounded above by μn < 3n-1, as compared to 2n-1 for the standard partial pivoting. This bound μn, close to 3n-2, is attainable for a class of near-singular matrices. Moreover, for the same matrices the growth factor is small under partial pivoting.

Original languageEnglish (US)
Pages (from-to)633-639
Number of pages7
JournalBIT Numerical Mathematics
Volume41
Issue number3
DOIs
StatePublished - Sep 2001

Keywords

  • Gaussian elimination
  • Growth factor
  • Parallel algorithm
  • Stability

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

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