Communication-optimal parallel and sequential QR and LU factorizations

Details Communication-optimal parallel and sequential QR and LU factorizations Communication-optimal parallel and sequential QR and LU factorizations

2008-08-19

arxiv.org/abs/0808.2664v1

Mathematics

Numerical Analysis

Submitted to SIAM Journal of Scientific Computing

Scientific paper

We present parallel and sequential dense QR factorization algorithms that are both optimal (up to polylogarithmic factors) in the amount of communication they perform, and just as stable as Householder QR. We prove optimality by extending known lower bounds on communication bandwidth for sequential and parallel matrix multiplication to provide latency lower bounds, and show these bounds apply to the LU and QR decompositions. We not only show that our QR algorithms attain these lower bounds (up to polylogarithmic factors), but that existing LAPACK and ScaLAPACK algorithms perform asymptotically more communication. We also point out recent LU algorithms in the literature that attain at least some of these lower bounds.

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