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

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Applied Parallel Computing (PARA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2367))

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Abstract

We present recursive blocked algorithms for solving triangular two-sided 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. This is a continuation of the work presented at the PARA2000 conference ([9]), where we presented results for one-sided Sylvester-type matrix equations. The improvements for two-sided Sylvester-type matrix equations are remarkable, and make a substantial impact on solving unreduced matrix equations problems as well. Uniprocessor and SMP parallel performance results are presented and compared with results from existing LAPACK and SLICOT 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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Editors and Affiliations

  1. CSC, P.O. Box 405, 02101, Espoo, Finland

    Juha Fagerholm , Juha Haataja , Jari Järvinen , Mikko Lyly , Peter Råback  & Ville Savolainen , , , ,  & 

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© 2002 Springer-Verlag Berlin Heidelberg

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Jonsson, I., Kågström, B. (2002). Parallel Two-Sided Sylvester-Type Matrix Equation Solvers for SMP Systems Using Recursive Blocking. In: Fagerholm, J., Haataja, J., Järvinen, J., Lyly, M., Råback, P., Savolainen, V. (eds) Applied Parallel Computing. PARA 2002. Lecture Notes in Computer Science, vol 2367. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48051-X_30

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  • DOI: https://doi.org/10.1007/3-540-48051-X_30

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  • Print ISBN: 978-3-540-43786-4

  • Online ISBN: 978-3-540-48051-8

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