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Subspace-by-subspace preconditioners for structured linear systems

✍ Scribed by Michel J. Daydé; Jérôme P. Décamps; Nicholas I. M. Gould

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
263 KB
Volume
6
Category
Article
ISSN
1070-5325

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✦ Synopsis

We consider the iterative solution of symmetric positive-definite linear systems whose coefficient matrix may be expressed as the outer product of low-rank terms. We derive suitable preconditioners for such systems, and demonstrate their effectiveness on a number of test examples. We also consider combining these methods with existing techniques to cope with the commonly-occuring case where the coefficient matrix is the linear sum of elements, some of which are of very low rank.

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In this paper we consider the problem of approximating the solution of infinite linear systems, finitely expressed by a sparse coefficient matrix. We analyse an algorithm based on Krylov subspace methods embedded in an adaptive enlargement scheme. The management of the algorithm is not trivial, due