BIT Numerical Mathematics

, Volume 45, Issue 1, pp 159–179

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

Article

DOI: 10.1007/s10543-005-2642-z

Cite this article as:
Papadopoulos, A.T., Duff, I.S. & Wathen, A.J. Bit Numer Math (2005) 45: 159. doi:10.1007/s10543-005-2642-z

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.

Keywords

preconditioningsparse linear systemssparse least-squaresiterative methodsincomplete orthogonal factorizationsGivens rotations

Copyright information

© Springer 2005

Authors and Affiliations

  • A. T. Papadopoulos
    • 1
  • I. S. Duff
    • 2
  • A. J. Wathen
    • 1
  1. 1.Oxford University Computing LaboratoryOxfordUK
  2. 2.Atlas CentreRutherford Appleton LaboratoryChilton, OxonEngland, UK