@Article{JCM-22-6,
author = {Zhongzhi, Bai and Li, Guiqing and Lu, Linzhang},
title = {Combinative Preconditioners of Modified Incomplete Cholesky Factorization and Sherman-Morrison-Woodbury Update for Self-Adjoint Elliptic Dirichlet-Periodic Boundary Value Problems},
journal = {Journal of Computational Mathematics},
year = {2004},
volume = {22},
number = {6},
pages = {833--856},
abstract = {<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>},
issn = {1991-7139},
doi = {https://doi.org/2004-JCM-10288},
url = {https://global-sci.com/article/85268/combinative-preconditioners-of-modified-incomplete-cholesky-factorization-and-sherman-morrison-woodbury-update-for-self-adjoint-elliptic-dirichlet-periodic-boundary-value-problems}
}