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Title: Communication-avoiding symmetric-indefinite factorization

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=PLTL TP T 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. As a result, the current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal.
 [1] ;  [2] ;  [3] ;  [4] ;  [5] ;  [6] ;  [3] ;  [6] ;  [2]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  2. Univ. of Tennessee, Knoxville, TN (United States)
  3. Univ. of California, Berkeley, CA (United States)
  4. Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Manchester (United Kingdom)
  5. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  6. Tel Aviv Univ., Tel Aviv (Israel)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0895-4798; 579666
Grant/Contract Number:
Accepted Manuscript
Journal Name:
SIAM Journal on Matrix Analysis and Applications
Additional Journal Information:
Journal Volume: 35; Journal Issue: 4; Journal ID: ISSN 0895-4798
Research Org:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; symmetric-indefinite matrices; communication-avoiding algorithms; Aasen's factorization