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Recursive formulation of Cholesky algorithm in Fortran 90

  • Jerzy Waśniewski
  • Bjarne Stig Andersen
  • Fred Gustavson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1541)

Abstract

Fortran 90 allows writing recursive procedures (see [7]). Recursion leads to automatic variable blocking for dense linear-algebra algorithms (see [5, 8]). The recursive way of programming algorithms eliminate the use of BLAS level 2 in the factorization steps. For this and other reasons recursion usually speed up the algorithms.

The formulation of the Cholesky factorization algorithm using recursion in Fortran 90 is presented in this paper.

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References

  1. 1.
    E. Anderson, Z. Bai, C. H. Bischof, J. Demmel, J. J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov and D. C. Sorensen. LAPACK Users’ Guide Release 2.0 SIAM, Philadelphia, 1995.Google Scholar
  2. 2.
    J.W. Demmel. Applied Numerical Linear Algebra. SIAM, Philadelphia, 1997.Google Scholar
  3. 3.
    J. Dongarra, and J. Waśniewski. High Performance Linear Algebra Package—LAPACK90. Lawn number 134: http://www.netlib.org/lapack/lawns/lawn134.ps Report UNIC-98-01, UNI•C, Lyngby, Denmark, 1998. Report ut-cs-98-384, University of Tennessee, Computer Science Department, Knoxville, April, 1998.Google Scholar
  4. 4.
    G.H. Golub and C.F. Van Loan. Matrix Computations. Johns Hopkins University Press Baltimore, MD, Any ed. from 1983.Google Scholar
  5. 5.
    F.G. Gustavson. Recursive Leads to Automatic Variable Blocking for Dense Linear-Algebra Algorithms. IBM Journal of Research and Development, Volume 41, Number 6, November 1997.Google Scholar
  6. 6.
    F.G. Gustavson, A. Henriksson, I. Jonsson, B. Kågström and P. Ling. Superscalar GEMM-based Level 3 BLAS—The On-going Evolution of a Portable and High-Performance Library. This Proceedings, Springer Verlag, 1998.Google Scholar
  7. 7.
    S. Metcalf and J. Reid. Fortran 90/95 Explained. Oxford, New York, Tokyo, Oxford University Press, 1996.Google Scholar
  8. 8.
    S. Toledo. Locality of Reference in LU Decomposition with Partial Pivoting. SIAM Journal on Matrix Analysis and Applications, vol. 18, No. 4, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jerzy Waśniewski
    • 1
  • Bjarne Stig Andersen
    • 1
  • Fred Gustavson
    • 2
  1. 1.The Danish Computing Centre for Research and Education (UNI⊙C)Technical University of DenmarkLyngbyDenmark
  2. 2.IBM T.J. Watson Research CenterYorktown HeightsUSA

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