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A Class of Incomplete Orthogonal Factorization Methods. II: Implementation and Results

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Abstract

We present, implement and test several incomplete QR factorization methods based on Givens rotations for sparse square and rectangular matrices. For square systems, the approximate QR factors are used as right-preconditioners for GMRES, and their performance is compared to standard ILU techniques. For rectangular matrices corresponding to linear least-squares problems, the approximate R factor is used as a right-preconditioner for CGLS. A comprehensive discussion is given about the uses, advantages and shortcomings of the preconditioners.

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Authors and Affiliations

  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK

    A. T. Papadopoulos & A. J. Wathen

  2. Atlas Centre, Rutherford Appleton Laboratory, Chilton, Oxon, OX11 0QX, England, UK

    I. S. Duff

Authors
  1. A. T. Papadopoulos
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  2. I. S. Duff
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  3. A. J. Wathen
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Corresponding author

Correspondence to A. T. Papadopoulos.

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AMS subject classification (2000)

65F10, 65F25, 65F50.

Received May 2002. Revised October 2004. Communicated by Åke Björck.

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Papadopoulos, A.T., Duff, I.S. & Wathen, A.J. A Class of Incomplete Orthogonal Factorization Methods. II: Implementation and Results. Bit Numer Math 45, 159–179 (2005). https://doi.org/10.1007/s10543-005-2642-z

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