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Adaptive procedure for estimating parameters for the nonsymmetric Tchebychev iteration

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Summary

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.

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Authors and Affiliations

  1. Applied Mathematics Division 8325, Sandia Laboratories, 94550, Livermore, CA, USA

    Thomas A. Manteuffel

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  1. Thomas A. Manteuffel
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This work was supported in part by the National Science Foundation under grants NSF GJ-36393 and DCR 74-23679 (NSF)

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Manteuffel, T.A. Adaptive procedure for estimating parameters for the nonsymmetric Tchebychev iteration. Numer. Math. 31, 183–208 (1978). https://doi.org/10.1007/BF01397475

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  • DOI: https://doi.org/10.1007/BF01397475

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