S-SDD 矩阵和SB-矩阵扩展垂直线性互补问题的全局误差界估计

大理大学学报 ›› 2026, Vol. 11 ›› Issue (6): 1-10.

• 数学与计算机科学 • 下一篇

S-SDD 矩阵和SB-矩阵扩展垂直线性互补问题的全局误差界估计

贵州民族大学数据科学与信息工程学院，贵阳　550025

出版日期:2026-06-15 发布日期:2026-06-30
基金资助:
贵州省科学技术基金项目（GCC2023027）;贵州省教育厅自然科学基金项目（QJJ2023012）；贵州民族大学科研基金项目（GZMUZK〔2023〕YB10）

Global Error Bound Estimation for the Extended Vertical Linear Complementarity Problem of S-SDD Matrix and SB-Matrix

College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China

Online:2026-06-15 Published:2026-06-30

摘要/Abstract

摘要： 扩展垂直线性互补问题是线性互补问题的一种推广，在工程学、经济学、控制论等领域有重要应用。借助S-SDD 矩阵和 SB-矩阵逆的无穷范数的上界，结合不等式放缩技巧，分别给出S-SDD 矩阵和 SB-矩阵的扩展垂直线性互补问题全局误差界的新估计式，改进了已有的结果。数值算例验证了新估计式的有效性。

关键词: 扩展垂直线性互补问题, 线性互补问题；S-SDD 矩阵, SB-矩阵;误差界

Abstract: The extended vertical linear complementarity problem is a generalization of the linear complementarity problem and has important applications in fields such as engineering, economics, and control theory. By leveraging the upper bounds of the infinity norms of the inverse of S-SDD matrices and SB-matrices, combined with inequality amplification techniques, new estimation formulas for the global error bound of the extended vertical linear complementarity problems of S-SDD matrices and SB-matrices are derived, improving upon existing results. Numerical examples validate the effectiveness of the new estimation formulas.

Key words: extended vertical linear complementarity problem, linear complementarity problem, S-SDD matrix, SB-matrix, error bound

中图分类号:

O151.21

王　峰, 周家冰. S-SDD 矩阵和SB-矩阵扩展垂直线性互补问题的全局误差界估计[J]. 大理大学学报, 2026, 11(6): 1-10.

Wang Feng, Zhou Jiabing. Global Error Bound Estimation for the Extended Vertical Linear Complementarity Problem of S-SDD Matrix and SB-Matrix[J]. Journal of Dali University, 2026, 11(6): 1-10.

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S-SDD 矩阵和SB-矩阵扩展垂直线性互补问题的全局误差界估计

Global Error Bound Estimation for the Extended Vertical Linear Complementarity Problem of S-SDD Matrix and SB-Matrix

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