On preconditioned Uzawa methods and SOR methods for saddle-point problems |
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Authors: | Xiaojun Chen |
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Affiliation: | Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan |
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Abstract: | 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. |
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Keywords: | Saddle-point problem Nonsmooth equation Uzawa method Precondition SOR method |
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