BIT Numerical Mathematics

, Volume 45, Issue 1, pp 159–179

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


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


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.


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