|Title||Communication-Avoiding Symmetric-Indefinite Factorization|
|Publication Type||Journal Article|
|Year of Publication||2014|
|Authors||Ballard, G., D. Becker, J. Demmel, J. Dongarra, A. Druinsky, I. Peled, O. Schwartz, S. Toledo, and I. Yamazaki|
|Journal||SIAM Journal on Matrix Analysis and Application|
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 = P LT L T P 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.
Communication-Avoiding Symmetric-Indefinite Factorization
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