A modified damped Newton method for linear complementarity problems

被引：20

作者：

Bai, Zhong-Zhi ^{[1
]}

Dong, Jun-Liang ^{[1
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China

来源：

NUMERICAL ALGORITHMS | 2006年 / 42卷 / 3-4期

关键词：

linear complementarity problems; damped Newton method; inexact splitting method; nondegenerate matrix; H-matrix;

D O I：

10.1007/s11075-006-9028-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a modified damped Newton method for solving large sparse linear complementarity problems, which adopts a new strategy for determining the stepsize at each Newton iteration. The global convergence of the new method is proved when the system matrix is a nondegenerate matrix. We then apply the matrix splitting technique to this new method, deriving an inexact splitting method for the linear complementarity problems. The global convergence of the resulting inexact splitting method is proved, too. Numerical results show that the new methods are feasible and effective for solving the large sparse linear complementarity problems.

引用

页码：207 / 228

页数：22

共 33 条

[1] Asynchronous multisplitting two-stage iterations for systems of weakly nonlinear equations [J].

Bai, ZZ ;

Huang, YG .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1998, 93 (01) :13-33

[2] Asynchronous parallel nonlinear multisplitting relaxation methods for large sparse nonlinear complementarity problems [J].

Bai, ZZ .

APPLIED MATHEMATICS AND COMPUTATION, 1998, 92 (01) :85-100

[3]

Bai ZZ, 2003, J COMPUT MATH, V21, P773

[4] Hermitian and skew-Hermitian splitting methods for non-hermitian positive definite linear systems [J].

Bai, ZZ ;

Golub, GH ;

Ng, MK .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2003, 24 (03) :603-626

[5] The convergence of parallel iteration algorithms for linear complementarity problems [J].

Bai, ZZ .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1996, 32 (09) :1-17

[6] Chaotic iterative methods for the linear complementarity problems [J].

Bai, ZZ ;

Evans, DJ .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1998, 96 (02) :127-138

[7] Matrix multisplitting methods with applications to linear complementarity problems: Parallel asynchronous methods [J].

Bai, ZZ ;

Evans, DJ .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2002, 79 (02) :205-232

[8]

Bai ZZ, 2002, J COMPUT MATH, V20, P97

[9] On the convergence of the multisplitting methods for the linear complementarity problem [J].

Bai, ZZ .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1999, 21 (01) :67-78

[10] Matrix multisplitting relaxation methods for linear complementarity problems [J].

Bai, ZZ ;

Evans, DJ .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1997, 63 (3-4) :309-326

← 1 2 3 4 →