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

Xiaojun Chen

doi:10.1016/S0377-0427(98)00197-6

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

Xiaojun Chen

Research output: Journal article publication › Journal article › Academic research › peer-review

33 Citations (Scopus)

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.

Original language	English
Pages (from-to)	207-224
Number of pages	18
Journal	Journal of Computational and Applied Mathematics
Volume	100
Issue number	2
DOIs	https://doi.org/10.1016/S0377-0427(98)00197-6
Publication status	Published - 21 Dec 1998
Externally published	Yes

Keywords

Nonsmooth equation
Precondition
Saddle-point problem
SOR method
Uzawa method

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

More information

10.1016/S0377-0427(98)00197-6

Cite this

@article{fb3504b15f8448388de2f741f26dc302,

title = "On preconditioned Uzawa methods and SOR methods for saddle-point problems",

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.",

keywords = "Nonsmooth equation, Precondition, Saddle-point problem, SOR method, Uzawa method",

author = "Xiaojun Chen",

year = "1998",

month = dec,

day = "21",

doi = "10.1016/S0377-0427(98)00197-6",

language = "English",

volume = "100",

pages = "207--224",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier B.V.",

number = "2",

}

TY - JOUR

T1 - On preconditioned Uzawa methods and SOR methods for saddle-point problems

AU - Chen, Xiaojun

PY - 1998/12/21

Y1 - 1998/12/21

N2 - 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.

AB - 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.

KW - Nonsmooth equation

KW - Precondition

KW - Saddle-point problem

KW - SOR method

KW - Uzawa method

UR - http://www.scopus.com/inward/record.url?scp=0032304985&partnerID=8YFLogxK

U2 - 10.1016/S0377-0427(98)00197-6

DO - 10.1016/S0377-0427(98)00197-6

M3 - Journal article

SN - 0377-0427

VL - 100

SP - 207

EP - 224

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

More information

Other files and links

Fingerprint

Cite this