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The Journal of Supercomputing

, Volume 4, Issue 4, pp 357–371 | Cite as

Using Strassen's algorithm to accelerate the solution of linear systems

  • David H. Bailey
  • King Lee
  • Horst D. Simon
Article

Abstract

Strassen's algorithm for fast matrix-matrix multiplication has been implemented for matrices of arbitrary shapes on the CRAY-2 and CRAY Y-MP supercomputers. Several techniques have been used to reduce the scratch space requirement for this algorithm while simultaneously preserving a high level of performance. When the resulting Strassen-based matrix multiply routine is combined with some routines from the new LAPACK library, LU decomposition can be performed with rates significantly higher than those achieved by conventional means. We succeeded in factoring a 2048 × 2048 matrix on the CRAY Y-MP at a rate equivalent to 325 MFLOPS.

Key words

Strassen's algorithm fast matrix multiplication linear systems LAPACK vector computers AMS Subject Classification 65F05 65F30 68A20 CR Subject Classification F.2.1 G.1.3 G.4 

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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • David H. Bailey
    • 1
  • King Lee
    • 2
  • Horst D. Simon
    • 3
  1. 1.NASA Ames Research CenterMoffett FieldUSA
  2. 2.Computer Science DepartmentCalifornia State UniversityBakersfieldUSA
  3. 3.Computer Sciences Corporation, NASA Ames Research CenterMoffett FieldUSA

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