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Parallel QR factorization of block-tridiagonal matrices

Abstract : In this work, we deal with the QR factorization of block-tridiagonal matrices, where the blocks are dense and rectangular. This work is motivated by a novel method for computing geodesics over Riemannian man-ifolds. If blocks are reduced sequentially along the diagonal, only limited parallelism is available. We propose a matrix permutation approach based on the Nested Dissection method which improves parallelism at the cost of additional computations and storage. We provide a detailed analysis of the approach showing that this extra cost is bounded. Finally, we present an implementation for shared memory systems relying on task parallelism and the use of a runtime system. Experimental results support the conclusions of our analysis and show that the proposed approach leads to good performance and scalability.
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Submitted on : Thursday, November 5, 2020 - 5:28:51 PM
Last modification on : Wednesday, November 3, 2021 - 5:26:10 AM

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Alfredo Buttari, Søren Hauberg, Costy Kodsi. Parallel QR factorization of block-tridiagonal matrices. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2020, 42 (6), pp.C313-C334. ⟨10.1137/19M1306166⟩. ⟨hal-02370953v2⟩

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