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Circulant preconditioners for solving singular perturbation delay differential equations
Author(s) -
Jin XiaoQing,
Lei SiuLong,
Wei YiMin
Publication year - 2004
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/nla.420
Subject(s) - generalized minimal residual method , preconditioner , mathematics , circulant matrix , eigenvalues and eigenvectors , invertible matrix , linear system , mathematical analysis , algorithm , pure mathematics , physics , quantum mechanics
We consider the solution of singular perturbation delay differential equations (SPDDEs) by using boundary value methods (BVMs). These methods require the solution of some nonsymmetric, large and sparse linear systems. The GMRES method with the Strang‐type block‐circulant preconditioner is proposed for solving these linear systems. We prove that if an A k 1, k 2‐stable BVM is used for solving a system of SPDDEs, then our preconditioner is invertible and the eigenvalues of the preconditioned system are clustered. When the GMRES method is applied to the preconditioned systems, the method would converge fast. Numerical results are given to show the effectiveness of our methods. Copyright © 2004 John Wiley & Sons, Ltd.