有关一类H_+矩阵线性互补问题的修正模系矩阵分裂迭代方法

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英文篇名：A Modified General Modulus-based Matrix Splitting Method for Linear Complementarity Problems of H_+-matrices 作者：朱磊 ; 徐玮玮 ; 殷俊锋 英文作者：ZHU LEI;XU WEIWEI;YIN JUNFENG;Nanjing Agricultural University;School of Mathematics and Statistics,Nanjing University of Information Science and Technology;School of Mathematical Sciences, Tongji University; 关键词：线性互补问题 ; 模系矩阵分裂迭代方法 ; H_+矩阵 英文关键词：linear complementarity problem;;modulus-based matrix splitting method;;H_+-matrix 中文刊名：YYSU 英文刊名：Acta Mathematicae Applicatae Sinica 机构：南京农业大学工学院;南京信息工程大学数学与统计学院;同济大学数学科学学院; 出版日期：2019-01-15 出版单位：应用数学学报 年：2019 期：v.42 基金：国家自然科学基金(U1733201,U1533202)项目经费;; 江苏省自然科学青年基金(BK20130985)资助项目 语种：中文; 页：YYSU201901009 页数：10 CN：01 ISSN：11-2040/O1 分类号：113-122

摘要

我们在本文建立了一类H+矩阵线性互补问题的修正模系矩阵分裂迭代方法并且给出了其收敛性分析.此外,我们也考虑了在给定方法下的最优参数选取问题.我们得出的修正方法是对[Xu W W, Liu H, A modified general modulus-based matrix splitting method for linear complementarity problems of H-matrices, Linear Algebra. Appl., 2014, 458:626-637]中方法2.1的一个修正.同时,我们也对[Xu W W,Modified modulus-based matrix splitting iteration methods for linear complementarity problems, Numer. Linear Algebra. Appl., 2015, 5:748-760]中方法3.1和方法3.2有关解的等价性证明作了补充说明.最后,我们给出的数值例子也表明了修正方法的有效性.
        In this paper we establish a modified general modulus-based matrix splitting iteration method for solving the large sparse linear complementarity problems of H_+-matrix and present the convergence analysis. In addition, the optimal parameters are considered under the given methods and we supplement the proof of equivalence of(z,r) from Methods3.1 and 3.2 in [2] and the solution of the original linear complementary problem LCP(q, A).Finally, we give a numerical example, which illustrates that the modified method is efficient.

引文

[1] Xu W W, Liu H. A modified general modulus-based matrix splitting method for linear complementarity problems of H-matrices. Linear Algebra, Appl.,2014, 458:626-637
    [2] Xu W W. Modified modulus-based matrix splitting iteration methods for linear complementarity problems. Numer. Linear Algebra. Appli, 2015, 5:748-760
    [3] Bai Z Z. On the convergence of the multisplitting methods for the linear complementarity problem.SIAM. J. Matrix Anal. Appl., 1999, 21:67-78
    [4] Bai Z Z. Modulus-based matrix splitting iteration methods for linear complementarity problems.Numer. Linear Algebra. Appl., 2010, 17:917-933
    [5] Bai Z Z. On the monotone convergence of matrix multisplitting relaxation methods for the linear complementarity problem. IMA J. Numer. Anal.,1998, 18:509-518
    [6] Li W. A general modulus-based matrix splitting iteration method for linear complementarity problems of H-matrices. Appl. Math. Lett., 2013, 26:1159-1164
    [7] Bai Z Z, Evans D J. Matrix multisplitting methods with applications to linear complementarity problems:Parallel asynchronous methods. Intern. J. Computer Math., 2002, 79:205-232
    [8] Bai Z Z, Zhang L L. Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems. Numer. Algorithms., 2013, 62:59-77
    [9] Bai Z Z, Zhang L L. Modulus-based synchronous multisplitting iteration methods for linear complementarity problems. Numer. Linear Algebra. Appl., 2013, 20:425-439
    [10] Hadjidimos A, Tzoumas M. Nonstationary extrapolated modulus algorithms for the solution of the linear complementarity problem. Linear Algebra Appl., 2009, 431:197-210
    [11] Bhatia R, Matrix Analysis. New York:Springer-Verlag 1997
    [12] Berman A, Plemmons R J. Nonnegative Matrices in the Mathematical Sciences. Philadelphia:SIAM Publisher, 1994
    [13] Zheng N, Yin J F. Accelerated modulus-based matrix splitting methods for linear complementarity problem. Numer. Algorithms, 2013, 64:245-262
    [14] Zheng N, Yin J F. Convergence of accelerated modulus-based matrix splitting iteration methods for linear complementarity problem with an H-matrix. J. Comput. Appl. Math., 2014, 260:281-293
    [15]郑宁,殷俊锋.基于不光滑边界的变系数抛物型方程的高精度紧格式.计算数学,2013, 35:275-285Zheng N, Yin J F. High order compact schemes for variable coefficient parabolic partial differential equations with non-smooth boundary conditions. Journal of Computational Mathematics, 2013, 35:275-285)
    [16] Cvetkovic L J. Some convergence conditions for a class of parallel decomposition-type linear relaxation methods. Appl. Numer. Math.,2002, 41:81-87
    [17] Cvetkovic L J. New subclasses of block H-matrices with applications to parallel decomposition-type relaxation methods. J. Numer. Algorithms, 2006, 42:325-334
    [18] Cvetkovic L J, Pena J M. Minimal sets alternative to minimal Gersgorin sets. Appl. Numer. Math.,2010, 60:442-451
    [19] Dong J L, Jiang M Q. modified modulus method for symmetric positive-definite linear complementarity problems. Numer. Linear Algebra. Appl.,2009, 16:129-143
    [20] Zhang L L, Ren Z R. Improved convergence theorems of modulus-based matrix splitting iterationmethods for linear complementarity problems. Appl. Math. Lett.,2013, 26:638-642
    [21] Li W, Zheng H. A preconditioned modulus-based iteration method for solving linear complementarity problems of H-matrices. Linear Multilinear Algebra., 2016, 7:1390-1403
    [22] Xu W W, Zhu L, Corrigendum to"A modified general modulus-based matrix splitting method for linear complementarity problems of H-matrices". Linear Algebra Appl.,2019,561:204-206