On hybrid iterative methods for nonsymmetric systems
of linear equations |
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Authors: | Thomas A Manteuffel Gerhard Starke |
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Institution: | Program in Applied Mathematics, Campus Box 526,
University of Colorado at Boulder, Boulder, CO 80309-0526, USA;
e-mail: tmanteuf@boulder.colorado.edu, US Institut für Praktische Mathematik, Universit?t Karlsruhe,
Englerstrasse 2, D-76128 Karlsruhe, Germany;
e-mail: starke@math.uni-karlsruhe.de, DE
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Abstract: | Summary.
Hybrid methods for the solution of systems of linear equations
consist of a first phase where some information about the associated
coefficient matrix is acquired, and a second phase in which a
polynomial iteration designed with respect to this information is
used. Most of the hybrid algorithms proposed recently for the
solution of nonsymmetric systems rely on the direct use of
eigenvalue estimates constructed by the Arnoldi process in Phase I.
We will show the limitations of this approach and propose an
alternative, also based on the Arnoldi process, which approximates
the field of values of the coefficient matrix and of its inverse in
the Krylov subspace. We also report on numerical experiments
comparing the resulting new method with other hybrid algorithms.
Received May 27, 1993 / Revised version received
November 14, 1994 |
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Keywords: | Mathematics Subject Classification (1991):65F10 |
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