B-矩阵线性互补问题误差界的上界序列

详细信息    查看全文 | 推荐本文 |

英文篇名：On Sequence of Upper Bounds for Linear Complementarity Problems of B-matrices 作者：孙德淑 ; 彭小平 ; 王峰 ; 徐玉梅 英文作者：SUN De-shu;PENG Xiao-ping;WANG Feng;XU Yu-mei;College of Data Science and Information Engineering, Guizhou Minzu University; 关键词：误差界 ; 线性互补问题 ; 对角占优矩阵 ; B-矩阵 英文关键词：error bound;;linear complementarity problem;;diagonally dominant matrix;;B-matrices 中文刊名：SSJS 英文刊名：Mathematics in Practice and Theory 机构：贵州民族大学数据科学与信息工程学院; 出版日期：2019-06-08 出版单位：数学的实践与认识 年：2019 期：v.49 基金：国家自然科学基金(11601473,11501141);; 贵州省科学技术基金([2019]1161,[2018]1079);; 贵州省教育厅自然科学基金([2015]420);; 贵州民族大学科研基金(2017YB068) 语种：中文; 页：SSJS201911019 页数：8 CN：11 ISSN：11-2018/O1 分类号：178-185

摘要

利用严格对角占优M-矩阵的逆矩阵的无穷大范数的范围,给出了B-矩阵线性互补问题解的误差界新的上界估计序列,理论证明了新估计式优于已有文献的结果.相应数值算例表明了结果的有效性.
        Based on the range for the infinity norm of inverse matrix of strictly diagonally dominant M-matrices, a estimation sequence of error bound for the linear complementarity problem is obtained when the involved matrix is a B-matrix. A numerical example is given to show that the new bound is better than some existing results.

引文

[1]Chen Xiaojun, Xiang Shuhuang. Perturbation bounds of P-matrix linear complementarity problems[J]. SIAM J Optim, 2007, 18(4):1250-1265.
    [2]Cottle R W, Pang Jongshi, Stone R E. The linear complementarity problem[M]. Academic Press,San Diego, 1992.
    [3]Murty K G. Linear Complementarity, Linear and nonlinear Programming[M]. Heldermann Verlag,'Berlin, 1998.
    [4]Pena J M. A class of P-matrices with applications to the localization of the eigenvalues of a real matrix[J]. SIAM J Matrix Anal Appl, 2001,22(4):1027-1037.
    [5].Chen Xiaojun, Xiang Shuhuang. Computation of error bounds for P-matrix linear complementarity problem[J]. Math Program, 2006, 106(3):513-525.
    [6]Chen Tingting, Li Wen, Wu Xiaoping, Vong S W. Error bounds for linear complementarity problems of MB-matrices[J]. Numer Algor, 2015, 70(2):341-356.
    [7]Dai Pingfan. Error bounds for linear complementarity problems of DB-matrices[J]. Linear Algebra Appl, 2011, 434(3):830-840.
    [8]Dai Pingfan, Lu Changjing, Li Yaotang. New error bounds for the linear complementarity problem with an SB-matrix[J].Numer Algor, 2013, 64(4):741-757.
    [9]Garcia-Esnaola M, Pena J M. Error bounds for linear complementarity problems for B-matrices[J].Appl Math Lett, 2009, 22(7):1071-1075.
    [10]GarciarEsnaola M, Pena J M. Error bounds for linear complementarity problems involving B~Smatrices[J]. Appl Math Lett, 2012, 25(10):1379-1383.
    [11]GarciarEsnaola M, Pena J M. B-Nekrasov matrices and error bounds for linear complementarity problems[J]. Numer Algor, 2016, 72(2):435-445.
    [12]Li Chaoqian, Li Yaotang. Note on error bounds for linear complementarity problems for B-matrices[J]. Appl Math Lett, 2016, 57(1):108-113.
    [13]Li Chaoqian, Li Yaotang. Weakly chained diagonally dominant B-matrices and error bounds for linear complementarity problems[J]. Numer Algor, 2016, 73(4):985-998.
    [14]Berman A, Plemmons R J. Nonnegative matrix in the mathematical sciences[M]. SIAM Publisher,Philadelphia, 1994.
    [15]Zhao Jianxing, Sang Caili. Estimation of the upper bound on‖A~(-1)‖_∞for strictly diagonally dominant M-matrix A[J]. Math Prac Theory, 2015, 45(16):284-289.