共查询到20条相似文献,搜索用时 843 毫秒
1.
In this paper, we propose a preconditioned general modulus-based matrix splitting iteration method for solving modulus equations arising from linear complementarity problems. Its convergence theory is proved when the system matrix is an H+-matrix, from which some new convergence conditions can be derived for the (general) modulus-based matrix splitting iteration methods. Numerical results further show that the proposed methods are superior to the existing methods. 相似文献
2.
Two-step modulus-based matrix splitting iteration method for linear complementarity problems 总被引:1,自引:0,他引:1
Li-Li Zhang 《Numerical Algorithms》2011,57(1):83-99
Bai has recently presented a modulus-based matrix splitting iteration method, which is a powerful alternative for solving
the large sparse linear complementarity problems. In this paper, we further present a two-step modulus-based matrix splitting
iteration method, which consists of a forward and a backward sweep. Its convergence theory is proved when the system matrix
is an H
+ -matrix. Moreover, for the two-step modulus-based relaxation iteration methods, more exact convergence domains are obtained
without restriction on the Jacobi matrix associated with the system matrix, which improve the existing convergence theory.
Numerical results show that the two-step modulus-based relaxation iteration methods are superior to the modulus-based relaxation
iteration methods for solving the large sparse linear complementarity problems. 相似文献
3.
关于线性互补问题的模系矩阵分裂迭代方法 总被引:1,自引:0,他引:1
模系矩阵分裂迭代方法是求解大型稀疏线性互补问题的有效方法之一.本文的目标是归纳总结模系矩阵分裂迭代方法的最新发展和已有成果,主要内容包括相应的多分裂迭代方法, 二级多分裂迭代方法和两步多分裂迭代方法, 以及这些方法的收敛理论. 相似文献
4.
Lili Zhang 《计算数学(英文版)》2015,33(1):100-112
To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based synchronous multisplitting iteration method and the corresponding symmetric modulus-based multisplitting relaxation methods. The convergence theorems are established when the system matrix is an $H_+$-matrix, which improve the existing convergence theory. Numerical results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation. 相似文献
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Li-Li Zhang 《Journal of Optimization Theory and Applications》2014,160(1):189-203
The matrix multisplitting iteration method is an effective tool for solving large sparse linear complementarity problems. However, at each iteration step we have to solve a sequence of linear complementarity sub-problems exactly. In this paper, we present a two-stage multisplitting iteration method, in which the modulus-based matrix splitting iteration and its relaxed variants are employed as inner iterations to solve the linear complementarity sub-problems approximately. The convergence theorems of these two-stage multisplitting iteration methods are established. Numerical experiments show that the two-stage multisplitting relaxation methods are superior to the matrix multisplitting iteration methods in computing time, and can achieve a satisfactory parallel efficiency. 相似文献
7.
本文我们利用预处理技术推广了求解线性互补问题的二步模基矩阵分裂迭代法,并针对H-矩阵类给出了新方法的收敛性分析,得到的理论结果推广了已有的一些方法. 相似文献
8.
针对系数矩阵为对称正定Toeplitz矩阵的线性互补问题,本文提出了一类预处理模系矩阵分裂迭代方法.先通过变量替换将线性互补问题转化为一类非线性方程组,然后选取Strang或T.Chan循环矩阵作为预优矩阵,利用共轭梯度法进行求解.我们分析了该方法的收敛性.数值实验表明,该方法是高效可行的. 相似文献
9.
为了改进求解大型稀疏线性互补问题模系多重网格方法的收敛速度和计算时间,本文采用加速模系超松弛(AMSOR)迭代方法作为光滑算子.局部傅里叶分析和数值结果表明此光滑算子能有效地改进模系多重网格方法的收敛因子、迭代次数和计算时间. 相似文献
10.
Hua Zheng 《Linear and Multilinear Algebra》2013,61(9):1773-1784
AbstractIn this paper, the convergence conditions of the two-step modulus-based matrix splitting and synchronous multisplitting iteration methods for solving linear complementarity problems of H-matrices are weakened. The convergence domain given by the proposed theorems is larger than the existing ones. 相似文献
11.
Numerical Algorithms - In this paper, for solving horizontal linear complementarity problems, a two-step modulus-based matrix splitting iteration method is established. The convergence analysis of... 相似文献
12.
Numerical Algorithms - In this paper, we discuss the modulus-based matrix splitting iteration method for solving a class of nonlinear complementarity problems under a weakened condition, and... 相似文献
13.
Global relaxed modulus-based synchronous block multisplitting multi-parameters methods for linear complementarity problems 下载免费PDF全文
Recently, Bai and Zhang [Numerical Linear Algebra with Applications, 20(2013):425439] constructed modulus-based synchronous multisplitting methods by an equivalent reformulation of the linear complementarity problem into a system of ?xed-point equations and studied the convergence of them; Li et al. [Journal of Nanchang University (Natural Science), 37(2013):307-312] studied synchronous block multisplitting iteration methods; Zhang and Li [Computers and Mathematics with Application, 67(2014):1954-1959] analyzed and obtained the weaker convergence results for linear complementarity problems. In this paper, we generalize their algorithms and further study global relaxed modulus-based synchronous block multisplitting multi-parameters methods for linear complementarity problems. Furthermore, we give the weaker convergence results of our new method in this paper when the system matrix is a block H+?matrix. Therefore, new results provide a guarantee for the optimal relaxation parameters, please refer to [A. Hadjidimos, M. Lapidakis and M. Tzoumas, SIAM Journal on Matrix Analysis and Applications, 33(2012):97-110, (dx.doi.org/10.1137/100811222)], where optimal parameters are determined. 相似文献
14.
本文构造了求解一类非线性互补问题的松弛two-sweep模系矩阵分裂迭代法. 理论分析建立了新方法在系数矩阵为正定矩阵或H+矩阵时的收敛性质.数值实验结果表明新方法是行之有效的, 并且在最优参数下松弛two-sweep模系矩阵分裂迭代法在迭代步数和时间上均优于传统的模系矩阵分裂迭代法和two-sweep模系矩阵分裂迭代法. 相似文献
15.
Accelerated modulus-based matrix splitting iteration methods for linear complementarity problem 总被引:1,自引:0,他引:1
For the large sparse linear complementarity problem, a class of accelerated modulus-based matrix splitting iteration methods is established by reformulating it as a general implicit fixed-point equation, which covers the known modulus-based matrix splitting iteration methods. The convergence conditions are presented when the system matrix is either a positive definite matrix or an H +-matrix. Numerical experiments further show that the proposed methods are efficient and accelerate the convergence performance of the modulus-based matrix splitting iteration methods with less iteration steps and CPU time. 相似文献
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To solve a class of nonlinear complementarity problems, accelerated modulus-based matrix splitting iteration methods are presented and analyzed. Convergence analysis and the choice of the parameters are given when the system matrix is either positive definite or an H +-matrix. Numerical experiments further demonstrate that the proposed methods are efficient and have better performance than the existing modulus-based iteration method in aspects of the number of iteration steps and CPU time. 相似文献
18.
本文提出了求解张量互补问题的一类光滑模系矩阵迭代方法.其基本思想是,先将张量互补问题转化为等价的模系方程组,然后引入一个逼近的光滑函数进行求解.我们分析了算法的收敛性,并通过数值实验验证了所提出算法的有效性. 相似文献
19.
Numerical Algorithms - In this paper, a class of two-step modulus-based matrix splitting (TMMS) iteration methods are proposed to solve the implicit complementarity problems. It is proved that the... 相似文献
20.
We weaken the convergence conditions of modulus-based matrix splitting and matrix two-stage splitting iteration methods for linear complementarity problems. Thus their applied scopes are further extended. 相似文献