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2005年07月06日

【期刊论文】Weighted max-norm estimate of additive Schwarz iteration scheme for solving linear complementarity problems☆

曾金平， Jin-Ping Zeng a， Dong-Hui Li a， Masao Fukushima b;*

Journal of Computational and Applied Mathematics 131(2001)1-14，-0001，（）：

-1年11月30日

In this paper, we consider an algebraic additive Schwarz iteration scheme for solving the 6nite-dimensional linear complementarity problem that involves an M-matrix. The scheme contains some existing algorithms as special cases. We establish monotone convergence of the iteration scheme under appropriate conditions. Moreover, using the concept of weak regular splitting, we estimate weighted max-norm bounds for iteration errors; thereby we show that the sequence generated by the iteration scheme converges to the unique solution of the problem without any restriction on the initial point.

Algebraic additive Schwarz iteration， Linear complementarity problem， Monotone convergence， Weighted max-norm

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2005年07月06日

【期刊论文】Generalized Schwarz Algorithm for Obstacle Problems

曾金平， S. ZHOU， J. ZENG AND X. TANG

Computers and Mathematics with Applications 38(1999)263-271，-0001，（）：

-1年11月30日

摘要

this paper, we present so-called generalized additive and multiplicative Schwarz algorithms for solving the discretization problems of obstacle problems with a self-adjoint elliptic operator. We establish convergence theorems for the proposed algorithms. Numerical tests show that a faster convergence rate can be obtained by choosing suitable parameters in the algorithms.

Variational inequalities,， Obstacle problems,， Generalized Schwarz algorithms,， Con-vergence.，

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2005年07月06日

【期刊论文】MONOTONIC ITERATIVE ALGORITHMS FOR A QUASICOMPLEMENTARITY PROBLEM*

曾金平， Shu-zi Zhou， Wu-ping Zan， Jin-ping Zeng

Journal of Computational Mathematics, Vol.19, No.3, 2001, 293-298.，-0001，（）：

-1年11月30日

摘要

We present two iterative algorithms, so called SCP and SA respectively, for soling quasicomplementarity problem (QCP). Algorithm SCP is to approximate QCP by a se-quence of ordinary complementarity problems(CP). SA is a Schwarz algorithm which can be implemented parllelly. We prove the algorithms above are monotonically convergent.

Quasicomplementarity problem,， Iterative algorthm,， Monotonic convergence,， Schwarz algorithm.，

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2005年07月06日

【期刊论文】Block monotone iterative methods for elliptic variational inequalities ☆

曾金平， Jinping Zeng， Shuzi Zhou *

Applied Mathematics and Computation 128(2002)109-127，-0001，（）：

-1年11月30日

摘要

This paper discusses some important block iterative methods for solving variational inequalities with a nonlinear operator and proves their monotone convergence properties and comparison theorems.These results extend C.V.Pao’s research work in Numer.Math.(72) (1995) 239 to variational inequalities. _ 2002 Elsevier Science Inc. All rights reserved.

Monotone iterative scheme， Upper solution， Lower solution， Comparison theorem， Variational inequality

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2005年07月06日

【期刊论文】Convergence Property of a Class of Variable Metric Methods

曾金平， ZHONG-ZHI ZHANG， Yiyang， Hunan， DING-HUA CAO AND JIN-PING ZENG*

Applied Mathematics Letters 17(2004)437-442，-0001，（）：

-1年11月30日

摘要

We investigate convergence property of the restricted Broyden class of variable metric methods. We show that when these methods with unit step are applied to a strictly convex quadratic objective function, the generated iterative sequence converges to the unique solution of the problem globally and superlinearly. Moreover, the distance between the iterative matrix and the Hessian matrix of the objective function decreases with iterations. The sequence of function vMues also exhibits descent property when the iteration is sufficiently large. (~) 2004 Elsevier Ltd. All rights reserved.

Variable metric methods,， Quadratic function.，

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