弱链对角占优 B- 矩阵线性互补问题解的误差界估计

doi:10.12288/szjs.s2020-0712

数值计算与计算机应用 ›› 2022, Vol. 43 ›› Issue (2): 154-162.DOI: 10.12288/szjs.s2020-0712

弱链对角占优 B- 矩阵线性互补问题解的误差界估计

董瑛雪, 莫宏敏, 周翠玲

吉首大学数学与统计学院, 吉首 416000

收稿日期:2020-11-14 发布日期:2022-06-10
通讯作者: 莫宏敏,Email:mohongmin@163.com.
基金资助:
国家自然科学基金(11461027)和湖南省教育厅科研基金(16A173)资助.

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董瑛雪, 莫宏敏, 周翠玲. 弱链对角占优 B- 矩阵线性互补问题解的误差界估计[J]. 数值计算与计算机应用, 2022, 43(2): 154-162.

Dong Yingxue, Mo Hongmin, Zhou Cuiling. ERROR BOUND ESTIMATION OF THE SOLUTION FOR LINEAR COMPLEMENTARITY PROBLEMS OF WEAKLY CHAINED DIAGONALLY DOMINANT B-MATRICES[J]. Journal on Numerica Methods and Computer Applications, 2022, 43(2): 154-162.

ERROR BOUND ESTIMATION OF THE SOLUTION FOR LINEAR COMPLEMENTARITY PROBLEMS OF WEAKLY CHAINED DIAGONALLY DOMINANT B-MATRICES

Dong Yingxue, Mo Hongmin, Zhou Cuiling

College of Mathematics and Statistics, Jishou University, Jishou 416000, China

Received:2020-11-14 Published:2022-06-10

通过利用弱链对角占优M-矩阵的逆矩阵的无穷大范数的范围,结合不等式的放缩技巧,给出弱链对角占优B-矩阵线性互补问题解的误差界新估计式.理论分析和数值算例均证明新的估计式改进了近期一些已有的结果.

关键词： 弱链对角占优B-矩阵, 线性互补问题, 误差界, B-矩阵。

By using the infinite norm range of the inverse matrix of the weakly diagonally dominant M-matrix, combined with the expansion and contraction techniques of the inequality, a new error bound estimator for the linear complementarity problem of weakly diagonally dominant B-matrix is given. Both theoretical analysis and numerical examples show that the new estimator improves some existing results.

Key words: Weakly chained diagonally dominant B-matrix, Linear complementarity problem, Error bounds, B-matrices.

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[1] Chen X J, Xiang S H. Perturbation bounds of P-matrix linear complementarity problems[J]. SIAM Journal on Optimization, 2007, 18(4):1250-1265.
[2] Cottle R W, Pang J S, Stone R E. The linear complementarity problem[M]. Boston:Academic Press, 1992.
[3] Murty K G. Linear complementarity, linear and nonlinear programming[M]. Berlin:Heldermann Verlag Press, 1988.
[4] Chen X J, Xiang S H. Computation of error bounds for P-matrix linear complementarity problem[J]. Mathematical Programming, 2006, 106(3):513-525.
[5] Shivakumar P N, Chew K H. A sufficient condition for nonvanishing of determinants[J]. Proceedings of the American Mathematical Society, 1974, 43(1):63-66.
[6] Peña J M. A Class of P-matrices with applications to the localization of the eigenvalues of a real matrix[J]. SIAM Journal on Matrix Analysis and Applications, 2001, 22(4):1027-1037.
[7] Li C Q, Li Y T. Weakly chained diagonally dominant B-matrices and error bounds for linear complementarity problems[J]. Numerical Algorithms, 2016, 73(4):985-998.
[8] Garc′ıa-Esnaola M, Peña J M. Error bounds for linear complementarity problems for B-matrices[J]. Applied Mathematics Letters, 2009, 22(7):1071-1075.
[9] Li C Q, Li Y T. Note on error bounds for linear complementarity problems for B-matrices[J]. Applied Mathematics Letters, 2016, 57(1):108-113.
[10] 赵仁庆,刘鹏.弱链对角占优M-矩阵的逆矩阵的无穷大范数的上界估计[J].楚雄师范学院学报, 2014, 29(03):5-10.

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摘要

弱链对角占优 B- 矩阵线性互补问题解的误差界估计

ERROR BOUND ESTIMATION OF THE SOLUTION FOR LINEAR COMPLEMENTARITY PROBLEMS OF WEAKLY CHAINED DIAGONALLY DOMINANT B-MATRICES

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