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 = PL^TLTP^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. The current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal.
Title
Communication-Avoiding Symmetric-Indefinite Factorization
Published
2013-07-05
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
EECS-2013-127
Type
Text
Extent
33 p
Archive
The Engineering Library
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