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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (4): 610-620.doi: 10.3969/j.issn.1005-3085.2022.04.009

• • 上一篇    下一篇

$M$ 矩阵的线性互补问题的误差界

房喜明   

  1. 肇庆学院数学与统计学院，肇庆 526000
  • 出版日期:2022-08-15 发布日期:2022-10-15
  • 基金资助:
    广东省基础与应用基础研究基金 (2022A1515011081)；肇庆学院创新团队项目；肇庆学院博士启动项目 (611-612279)；肇庆教育发展研究项目 (QJYY2020093).

The Error Bounds of the Linear Complementarity Problem with an $M$-matrix

FANG Ximing   

  1. School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526000
  • Online:2022-08-15 Published:2022-10-15
  • Supported by:
    The Guangdong Basic and Applied Basic Research Foundation (2022A1515011081); the Innovative Research Team Project of Zhaoqing University; the Zhaoqing University Research Program (611-612279); the Education and Development Project of Zhaoqing (QJYY2020093).

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摘要：

研究了线性互补问题的误差界。首先，利用主对角部分为单位矩阵的 $M$ 矩阵的一个函数，给出该类线性互补问题的误差界理论。之后，通过线性互补问题的模型转化，将误差界理论进行推广，给出系数矩阵为一般 $M$ 矩阵的线性互补问题的误差界。用低阶和高阶的例子对误差界理论进行了验证和比较。数值结果表明，提出的误差界理论是有效的和实用的。

关键词: 线性互补问题, $M$ 矩阵, 误差界

Abstract:

The error bounds of linear complementarity problems are studied. Firstly, the error bound theory of one kind of linear complementarity problems is presented by using a function of $M$-matrix whose main diagonal part is an identity matrix. Then, by transforming the model of linear complementarity problem, the error bound theory is generalized, and the error bound of linear complementarity problem whose system matrix is a general $M$-matrix is given. The error bound theory is verified and compared through low- and high-order examples. Numerical results show that the proposed error bound theory is effective and practical.

Key words: linear complementarity problem, $M$-matrix, error bound

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