An adaptive Chebyshev iterative method\newline for
nonsymmetric linear systems based on modified moments |
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Authors: | D Calvetti GH Golub L Reichel |
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Institution: | (1) Department of Pure and Applied Mathematics, Stevens Institute of Technology, Hoboken, NJ 07030, USA , US;(2) Department of Computer Science, Stanford University, Stanford, CA 94305, USA , US;(3) Department of Mathematics and Computer Science, Kent State University, Kent, OH 44242, USA , US |
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Abstract: | Summary.
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.
Received May 13, 1992/Revised version received May 13,
1993 |
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Keywords: | Mathematics Subject Classification (1991): 65F10 |
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