@article {815, title = {Communication-Avoiding Symmetric-Indefinite Factorization}, journal = {SIAM Journal on Matrix Analysis and Application}, volume = {35}, year = {2014}, month = {2014-07}, pages = {1364-1406}, abstract = {We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen{\textquoteright}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.}, keywords = {plasma}, author = {Grey Ballard and Dulceneia Becker and James Demmel and Jack Dongarra and Alex Druinsky and I Peled and Oded Schwartz and Sivan Toledo and Ichitaro Yamazaki} }