, Volume 45, Issue 1, pp 159-179

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

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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.

AMS subject classification (2000)

65F10, 65F25, 65F50.
Received May 2002. Revised October 2004. Communicated by Åke Björck.