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Subspace‐by‐subspace preconditioners for structured linear systems
Author(s) -
Daydé Michel J.,
Décamps Jérôme P.,
Gould Nicholas I. M.
Publication year - 1999
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(199904/05)6:3<213::aid-nla161>3.0.co;2-v
Subject(s) - coefficient matrix , mathematics , rank (graph theory) , subspace topology , krylov subspace , linear system , positive definite matrix , matrix (chemical analysis) , augmented matrix , iterative method , algorithm , mathematical optimization , combinatorics , symmetric matrix , square matrix , mathematical analysis , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , composite material
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. Copyright © 1999 John Wiley & Sons, Ltd.