Numerical Algorithms

, Volume 12, Issue 1, pp 125–149

An adaptive Richardson iteration method for indefinite linear systems

  • D. Calvetti
  • L. Reichel

DOI: 10.1007/BF02141745

Cite this article as:
Calvetti, D. & Reichel, L. Numer Algor (1996) 12: 125. doi:10.1007/BF02141745


An adaptive Richardson iteration method is presented for the solution of large linear systems of equations with a sparse, symmetric, nonsingular, indefinite matrix. The relaxation parameters for Richardson iteration are chosen to be reciprocal values of Leja points for a compact setK:=[a,b]∪[c,d], where [a,b] is an interval on the negative real axis and [c, d] is an interval on the positive real axis. Endpoints of these intervals are determined adaptively by computing certain modified moments during the iterations. Computed examples show that this adaptive Richardson method can be competitive with the SYMMLQ and the conjugate residual methods, which are based on the Lanczos process.

Copyright information

© J.C. Baltzer AG, Science Publishers 1996

Authors and Affiliations

  • D. Calvetti
    • 1
  • L. Reichel
    • 2
  1. 1.Department of Pure and Applied MathematicsStevens Institute of TechnologyHobokenUSA
  2. 2.Department of Mathematics and Computer ScienceKent State UniversityKentUSA