Communication-avoiding symmetric-indefinite factorization

Grey Ballard*, Dulceneia Becker, James Demmel, Jack Dongarra, Alex Druinsky, Inon Peled, Oded Schwartz, Sivan Toledo, Ichitaro Yamazaki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen's triangular tridiagonalization. It factors a dense symmetric matrix A as the product A = PLTLT PT , where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding factorization: it performs an asymptotically optimal amount of communication in a two-level memory hierarchy for almost any cache-line size. Adaptations of the algorithm to parallel computers are likely to be communication efficient as well; one such adaptation has been recently published. The current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal.

Original languageAmerican English
Pages (from-to)1364-1406
Number of pages43
JournalSIAM Journal on Matrix Analysis and Applications
Issue number4
StatePublished - 2014
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014 Society for Industrial and Applied Mathematics.


  • Aasen's factorization
  • Communication-avoiding algorithms
  • Symmetric-indefinite matrices


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