Numerische Mathematik

, Volume 31, Issue 2, pp 183–208 | Cite as

Adaptive procedure for estimating parameters for the nonsymmetric Tchebychev iteration

  • Thomas A. Manteuffel


An iteration based upon the Tchebychev polynomials in the complex plane can be used to solve large sparse nonsymmetric linear systems whose eigenvalues lie in the right half plane. The iteration depends upon two parameters which can be chosen from knowledge of the convex hull of the spectrum of the linear operator. This paper deals with a procedure based upon the power method for dynamically estimating the convex hull of the spectrum. The stability of the procedure is discussed in terms of the field of values of the operator. Results show the adaptive procedure to be an effective method of determining parameters. The Tchebychev iteration compares favorably with several competing iterative methods.

Subject Classifications

AMS(MOS): 65F10 CR: 5.14 


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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Thomas A. Manteuffel
    • 1
  1. 1.Applied Mathematics Division 8325Sandia LaboratoriesLivermoreUSA

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