On preconditioned Uzawa methods and SOR methods for saddle-point problems

[摘要] This paper studies convergence analysis of a preconditioned inexact Uzawa method for nondifferentiable saddle-point problems. The SOR-Newton method and the SOR-BFGS method are special cases of this method. We relax the Bramble-Pasciak-Vassilev condition on preconditioners for convergence of the inexact Uzawa method for linear saddle-point problems. The relaxed condition is used to determine the relaxation parameters in the SOR-Newton method and the SOR-BFGS method. Furthermore, we study global convergence of the multistep inexact Uzawa method for nondifferentiable saddle-point problems. (C) 1998 Elsevier Science B.V. All rights reserved.

[发布日期] 1998-12-21

[关键词] saddle-point problem;nonsmooth equation;Uzawa method;precondition;SOR method