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COMBINATIVE PRECONDITIONERS OF MODIFIED INCOMPLETE CHOLESKY FACTORIZATION AND SHERMAN-MORRISON-WOODBURY UPDATE FOR SELF-ADJOINT ELLIPTIC DIRICHLET-PERIODIC BOUNDARY VALUE PROBLEMS

Zhong-zhi Bai, Gui-qing Li and Lin-zhang Lu
Journal of Computational Mathematics
Vol. 22, No. 6 (NOVEMBER 2004), pp. 833-856
Stable URL: http://www.jstor.org/stable/43693210
Page Count: 24
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
COMBINATIVE PRECONDITIONERS OF MODIFIED INCOMPLETE CHOLESKY FACTORIZATION AND SHERMAN-MORRISON-WOODBURY UPDATE FOR SELF-ADJOINT ELLIPTIC DIRICHLET-PERIODIC BOUNDARY VALUE PROBLEMS
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Abstract

For the system of linear equations arising from discretization of the second-order selfadjoint 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 O(h⁻¹), one order smaller than the condition number 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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