The growth-factor bound for the Bunch-Kaufman factorization is tight

Alex Druinsky*, Sivan Toledo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We show that the growth-factor bound in the Bunch-Kaufman factorization method is essentially tight. The method factors a symmetric matrix A into A = PTLDLTP, where P is a permutation matrix, L is lower triangular, and D is block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The method uses one of several partial pivoting rules that ensure bounded in the elements of the reduced matrix and the factor D (growth in L is not bounded).We show that the exponential bound is essentially tight, thereby solving a question that has been open since 1977.

Original languageEnglish
Pages (from-to)928-937
Number of pages10
JournalSIAM Journal on Matrix Analysis and Applications
Volume32
Issue number3
DOIs
StatePublished - 2011

Keywords

  • Bunch-Kaufman factorization
  • Growth factor
  • Numerical stability
  • Symmetric indefinite matrices

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