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International Journal of Parallel Programming

, Volume 32, Issue 6, pp 501–523 | Cite as

Look Left, Look Right, Look Left Again: An Application of Fractal Symbolic Analysis to Linear Algebra Code Restructuring

  • Vijay Menon
  • Keshav Pingali
Article

Abstract

Fractal symbolic analysis is a symbolic analysis technique for verifying the legality of program transformations. It is strictly more powerful than dependence analysis; for example, it can be used to verify the legality of blocking LU factorization with pivoting, a task for which dependence analysis is inadequate. In this paper, we show how fractal symbolic analysis can be used to convert between left- and right-looking versions of three kernels of central importance in computational science: triangular solve, Cholesky factorization, and LU factorization with pivoting.

Program restructuring symbolic analysis numerical methods high-performance computing 

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Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • Vijay Menon
    • 1
  • Keshav Pingali
    • 2
  1. 1.Microprocessor Technology LabIntel CorporationSanta ClaraU.S.A
  2. 2.Department of Computer ScienceCornell UniversityU.S.A

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