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Parallel Triangular Sylvester-Type Matrix Equation Solvers for SMP Systems Using Recursive Blocking

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Applied Parallel Computing. New Paradigms for HPC in Industry and Academia (PARA 2000)

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Abstract

We present recursive blocked algorithms for solving triangular Sylvester-type matrix equations. Recursion leads to automatic blocking that is variable and “squarish”. The main part of the computations are performed as level 3 general matrix multiply and add (GEMM) operations. We also present new highly optimized superscalar kernels for solving small-sized matrix equations stored in level 1 cache. Hereby, a larger part of the total execution time will be spent in GEMM operations. In turn, this leads to much better performance, especially for small to medium-sized problems, and improved parallel effciency on shared memory processor (SMP) systems. Uniprocessor and SMP parallel performance results are presented and compared with results from existing LAPACK routines for solving this type of matrix equations.

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Author information

Authors and Affiliations

  1. Department of Computing Science and HPC2N, Umeå University, SE-901 87, Umeå, Sweden

    Isak Jonsson & Bo Kågström

Authors
  1. Isak Jonsson
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  2. Bo Kågström
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, 5020, Bergen, Norway

    Tor Sørevik , Fredrik Manne  & Assefaw Hadish Gebremedhin ,  & 

  2. Parallab, University of Bergen, 5020, Bergen, Norway

    Randi Moe

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© 2001 Springer-Verlag Berlin Heidelberg

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Jonsson, I., Kågström, B. (2001). Parallel Triangular Sylvester-Type Matrix Equation Solvers for SMP Systems Using Recursive Blocking. In: Sørevik, T., Manne, F., Gebremedhin, A.H., Moe, R. (eds) Applied Parallel Computing. New Paradigms for HPC in Industry and Academia. PARA 2000. Lecture Notes in Computer Science, vol 1947. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-70734-4_10

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  • DOI: https://doi.org/10.1007/3-540-70734-4_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41729-3

  • Online ISBN: 978-3-540-70734-9

  • eBook Packages: Springer Book Archive

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