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

• 来源期刊: 计算数学(英文版)
• 关键词: System of linear equations Conjugate gradient method Incomplete Choleskyfactorization Sherman-Morrison-Woodbury formula Conditioning.
• 年，卷（期）: 2004,（6）
• 页码范围: 833-856
• 页数: 24页
• 语种: 英文

摘要

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 ShermanMorrison-Woodbury update. Theoretical analyses show that the condition numbers of the preconditioned matrices can be reduced to (h-1), one order smaller than the condition number (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.