Communication-optimal parallel and sequential QR and LU factorizations

Abstract

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.

Submitted to SIAM Journal of Scientific Computing

References in corpus (2)

• A Class of Parallel Tiled Linear Algebra Algorithms for Multicore Architectures
• Implementing Communication-Optimal Parallel and Sequential QR Factorizations

Cited by in corpus (4)

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• A hierarchically blocked Jacobi SVD algorithm for single and multiple graphics processing units
• Computing the R of the QR factorization of tall and skinny matrices using MPI_Reduce
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