Numerische Mathematik

, Volume 67, Issue 1, pp 21–40

An adaptive Chebyshev iterative method\newline for nonsymmetric linear systems based on modified moments

  • D. Calvetti
  • G.H. Golub
  • L. Reichel

DOI: 10.1007/s002110050016

Cite this article as:
Calvetti, D., Golub, G. & Reichel, L. Numer. Math. (1994) 67: 21. doi:10.1007/s002110050016


Large, sparse nonsymmetric systems of linear equations with a matrix whose eigenvalues lie in the right half plane may be solved by an iterative method based on Chebyshev polynomials for an interval in the complex plane. Knowledge of the convex hull of the spectrum of the matrix is required in order to choose parameters upon which the iteration depends. Adaptive Chebyshev algorithms, in which these parameters are determined by using eigenvalue estimates computed by the power method or modifications thereof, have been described by Manteuffel [18]. This paper presents an adaptive Chebyshev iterative method, in which eigenvalue estimates are computed from modified moments determined during the iterations. The computation of eigenvalue estimates from modified moments requires less computer storage than when eigenvalue estimates are computed by a power method and yields faster convergence for many problems.

Mathematics Subject Classification (1991): 65F10 

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • D. Calvetti
    • 1
  • G.H. Golub
    • 2
  • L. Reichel
    • 3
  1. 1.Department of Pure and Applied Mathematics, Stevens Institute of Technology, Hoboken, NJ 07030, USA US
  2. 2.Department of Computer Science, Stanford University, Stanford, CA 94305, USA US
  3. 3.Department of Mathematics and Computer Science, Kent State University, Kent, OH 44242, USA US

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