Numerical Algorithms

, Volume 25, Issue 1, pp 223–239

On the preconditioning of matrices with skew-symmetric splittings

  • Gene H. Golub
  • Denis Vanderstraeten

DOI: 10.1023/A:1016637813615

Cite this article as:
Golub, G.H. & Vanderstraeten, D. Numerical Algorithms (2000) 25: 223. doi:10.1023/A:1016637813615


The rates of convergence of iterative methods with standard preconditioning techniques usually degrade when the skew-symmetric part S of the matrix is relatively large. In this paper, we address the issue of preconditioning matrices with such large skew-symmetric parts. The main idea of the preconditioner is to split the matrix into its symmetric and skew-symmetric parts and to “invert” the (shifted) skew-symmetric matrix. Successful use of the method requires the solution of a linear system with matrix I+S. An efficient method is developed using the normal equations, preconditioned by an incomplete orthogonal factorization.

Numerical experiments on various systems arising in physics show that the reduction in terms of iteration count compensates for the additional work per iteration when compared to standard preconditioners.

preconditioning skew-symmetry incomplete orthogonal factorization 

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Gene H. Golub
    • 1
  • Denis Vanderstraeten
    • 2
  1. 1.Scientific Computing and Computational MathematicsStanford UniversityUSA
  2. 2.Department Computer ScienceKatholieke Universiteit LeuvenHeverleeBelgium

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