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 $A=PLTLT}PT},$ where $P$ is a permutation matrix, $L$ is lower triangular,...

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Vydané v:SIAM journal on matrix analysis and applications Ročník 35; číslo 4; s. 1364 - 1406
Hlavní autori: Ballard, Grey, Becker, Dulceneia, Demmel, James, Dongarra, Jack, Druinsky, Alex, Peled, Inon, Schwartz, Oded, Toledo, Sivan, Yamazaki, Ichitaro
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: United States SIAM 01.01.2014
Predmet:
Aasen's factorization
Adaptation
Algorithms
Asymptotic properties
Blocking
communication-avoiding algorithms
Factorization
Hierarchies
MATHEMATICS AND COMPUTING
Optimization
Parallel computers
symmetric-indefinite matrices
ISSN:0895-4798, 1095-7162
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Shrnutí: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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
AC04-94AL85000
USDOE National Nuclear Security Administration (NNSA)
SAND-2015-1851J
ISSN:0895-4798
1095-7162
DOI:10.1137/130929060