SOR-like methods for augmented systems

Gene H. Golub; X. Wu; Jin Yun Yuan

doi:10.1023/A:1021965717530

SOR-like methods for augmented systems

Gene H. Golub^*, X. Wu, Jin Yun Yuan

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

255 Citations (Scopus)

Abstract

Several SOR-like methods are proposed for solving augmented systems. These have many different applications in scientific computing, for example, constrained optimization and the finite element method for solving the Stokes equation. The convergence and the choice of optimal parameter for these algorithms are studied. The convergence and divergence regions for some algorithms are given, and the new algorithms are applied to solve the Stokes equations as well.

Original language	English
Pages (from-to)	71-85
Number of pages	15
Journal	BIT Numerical Mathematics
Volume	41
Issue number	1
DOIs	https://doi.org/10.1023/A:1021965717530
Publication status	Published - Mar 2001

User-Defined Keywords

Augmented system
Constrained optimization
Convergence
Finite element method
Navier-Stokes equation
Optimal parameter
SOR method
SOR-like methods

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10.1023/A:1021965717530

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title = "SOR-like methods for augmented systems",

abstract = "Several SOR-like methods are proposed for solving augmented systems. These have many different applications in scientific computing, for example, constrained optimization and the finite element method for solving the Stokes equation. The convergence and the choice of optimal parameter for these algorithms are studied. The convergence and divergence regions for some algorithms are given, and the new algorithms are applied to solve the Stokes equations as well.",

keywords = "Augmented system, Constrained optimization, Convergence, Finite element method, Navier-Stokes equation, Optimal parameter, SOR method, SOR-like methods",

author = "Golub, {Gene H.} and X. Wu and Yuan, {Jin Yun}",

note = "Funding Information: †T he work of the first author was partially supported by the National Science Foundation. T he work of the second author was supported by RGC of Hong Kong and FRG of Hong Kong Baptist University. T he work of the third author was partially supported by FUNPAR, CNPq and CAPES, Brazil.",

year = "2001",

month = mar,

doi = "10.1023/A:1021965717530",

language = "English",

volume = "41",

pages = "71--85",

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T1 - SOR-like methods for augmented systems

AU - Golub, Gene H.

AU - Wu, X.

AU - Yuan, Jin Yun

N1 - Funding Information: †T he work of the first author was partially supported by the National Science Foundation. T he work of the second author was supported by RGC of Hong Kong and FRG of Hong Kong Baptist University. T he work of the third author was partially supported by FUNPAR, CNPq and CAPES, Brazil.

PY - 2001/3

Y1 - 2001/3

N2 - Several SOR-like methods are proposed for solving augmented systems. These have many different applications in scientific computing, for example, constrained optimization and the finite element method for solving the Stokes equation. The convergence and the choice of optimal parameter for these algorithms are studied. The convergence and divergence regions for some algorithms are given, and the new algorithms are applied to solve the Stokes equations as well.

AB - Several SOR-like methods are proposed for solving augmented systems. These have many different applications in scientific computing, for example, constrained optimization and the finite element method for solving the Stokes equation. The convergence and the choice of optimal parameter for these algorithms are studied. The convergence and divergence regions for some algorithms are given, and the new algorithms are applied to solve the Stokes equations as well.

KW - Augmented system

KW - Constrained optimization

KW - Convergence

KW - Finite element method

KW - Navier-Stokes equation

KW - Optimal parameter

KW - SOR method

KW - SOR-like methods

UR - http://www.scopus.com/inward/record.url?scp=0041437231&partnerID=8YFLogxK

U2 - 10.1023/A:1021965717530

DO - 10.1023/A:1021965717530

M3 - Journal article

AN - SCOPUS:0041437231

SN - 0006-3835

VL - 41

SP - 71

EP - 85

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

IS - 1

ER -

SOR-like methods for augmented systems

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