On hybrid iterative methods for nonsymmetric systemsof linear equations |
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Authors: | Thomas A. Manteuffel Gerhard Starke |
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Affiliation: | 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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