TY - JOUR
T1 - Combinative Preconditioners of Modified Incomplete Cholesky Factorization and Sherman-Morrison-Woodbury Update for Self-Adjoint Elliptic Dirichlet-Periodic Boundary Value Problems
AU - Bai , Zhongzhi
AU - Li , Guiqing
AU - Lu , Linzhang
JO - Journal of Computational Mathematics
VL - 6
SP - 833
EP - 856
PY - 2004
DA - 2004/12
SN - 22
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/10288.html
KW - System of linear equations, Conjugate gradient method, Incomplete Cholesky
factorization, Sherman-Morrison-Woodbury formula, Conditioning.
AB - <p style="text-align: justify;">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 &nbsp;$\mathcal{O}(h^{-2})$ 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.</p>