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Title: Communication-avoiding symmetric-indefinite factorization

Journal Article · · SIAM Journal on Matrix Analysis and Applications
DOI:https://doi.org/10.1137/130929060· OSTI ID:1237467
 [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)
+ Show Author Affiliations

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=PLTLTPT 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.

Research Organization:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1237467
Report Number(s):
SAND-2015-1851J; 579666
Journal Information:
SIAM Journal on Matrix Analysis and Applications, Vol. 35, Issue 4; ISSN 0895-4798
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 11 works
Citation information provided by
Web of Science

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Cited By (1)

Non-GPU-resident symmetric indefinite factorization: Non-GPU-resident Dense Symmetric Indefinite Factorization journal November 2016

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Related Subjects

97 MATHEMATICS AND COMPUTING
symmetric-indefinite matrices
communication-avoiding algorithms
Aasen's factorization