Implementing Communication-Optimal Parallel and Sequential QR Factorizations

Details Implementing Communication-Optimal Parallel and Sequential QR Factorizations Implementing Communication-Optimal Parallel and Sequential QR Factorizations

2008-09-14

arxiv.org/abs/0809.2407v1

Mathematics

Numerical Analysis

Scientific paper

We present parallel and sequential dense QR factorization algorithms for tall and skinny matrices and general rectangular matrices that both minimize communication, and are as stable as Householder QR. The sequential and parallel algorithms for tall and skinny matrices lead to significant speedups in practice over some of the existing algorithms, including LAPACK and ScaLAPACK, for example up to 6.7x over ScaLAPACK. The parallel algorithm for general rectangular matrices is estimated to show significant speedups over ScaLAPACK, up to 22x over ScaLAPACK.

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