Combinative Preconditioners of Modified Incomplete Cholesky Factorization and Sherman-Morrison-Woodbury Update for Self-Adjoint Elliptic Dirichlet-Periodic Boundary Value Problems
Year: 2004
Author: Zhongzhi Bai, Guiqing Li, Linzhang Lu
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 6 : pp. 833–856
Abstract
For the system of linear equations arising from discretization of the second-order self-adjoint elliptic Dirichlet-periodic boundary value problems, by making use of the special structure of the coefficient matrix we present a class of combinative preconditioners which are technical combinations of modified incomplete Cholesky factorizations and Sherman-Morrison-Woodbury update. Theoretical analyses show that the condition numbers of the preconditioned matrices can be reduced to $\mathcal{O}(h^{-1})$, one order smaller than the condition number $\mathcal{O}(h^{-2})$ of the original matrix. Numerical implementations show that the resulting preconditioned conjugate gradient methods are feasible, robust and efficient for solving this class of linear systems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-JCM-10288
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 6 : pp. 833–856
Published online: 2004-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: System of linear equations Conjugate gradient method Incomplete Cholesky factorization Sherman-Morrison-Woodbury formula Conditioning.