A framework for polynomial preconditioners based on fast transforms I: Theory |
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Authors: | Sverker Holmgren Kurt Otto |
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Institution: | (1) Department of Scientific Computing, Uppsala University, Box 120, SE-751 04 Uppsala, Sweden |
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Abstract: | Optimal and superoptimal approximations of a complex square matrix by polynomials in a normal basis matrix are considered.
If the unitary transform associated with the eigenvectors of the basis matrix is computable using a fast algorithm, the approximations
may be utilized for constructing preconditioners. Theorems describing how the parameters of the approximations could be efficiently
computed are given, and for special cases earlier results by other authors are recovered. Also, optimal and superoptimal approximations
for block matrices are determined, and the same type of theorems as for the point case are proved.
This research was supported by the Swedish National Board for Industrial and Technical Development (NUTEK) and by the U.S.
National Science Foundation under grant ASC-8958544. |
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Keywords: | 65F99 65T20 |
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