刘毅, 井霞, 高磊. Ostrowski-Brauer Sparse B (OBS-B)矩阵及其线性互补问题的误差界[J]. 云南大学学报(自然科学版), 2021, 43(2): 205-213. doi: 10.7540/j.ynu.20200384
引用本文: 刘毅, 井霞, 高磊. Ostrowski-Brauer Sparse B (OBS-B)矩阵及其线性互补问题的误差界[J]. 云南大学学报(自然科学版), 2021, 43(2): 205-213. doi: 10.7540/j.ynu.20200384
LIU Yi, JING Xia, GAO Lei. Ostrowski-Brauer Sparse B (OBS-B) matrices and error bounds for linear complementarity problems[J]. Journal of Yunnan University: Natural Sciences Edition, 2021, 43(2): 205-213. DOI: 10.7540/j.ynu.20200384
Citation: LIU Yi, JING Xia, GAO Lei. Ostrowski-Brauer Sparse B (OBS-B) matrices and error bounds for linear complementarity problems[J]. Journal of Yunnan University: Natural Sciences Edition, 2021, 43(2): 205-213. DOI: 10.7540/j.ynu.20200384

Ostrowski-Brauer Sparse B (OBS-B)矩阵及其线性互补问题的误差界

Ostrowski-Brauer Sparse B (OBS-B) matrices and error bounds for linear complementarity problems

  • 摘要: P-矩阵在科学工程计算中发挥着重要作用. 基于Ostrowski-Brauer Sparse(OBS)矩阵的定义,引入一类新的P-矩阵子类——Ostrowski-Brauer Sparse B(OBS-B)矩阵,该矩阵类包含B-矩阵和DB-矩阵. 进一步,利用OBS矩阵逆的无穷大范数估计式,给出了OBS-B矩阵线性互补问题的误差界,并证明了在一定条件下所给误差界优于García-Esnaola和Peña给出的经典误差界. 最后,通过数值算例对所得结果进行了说明.

     

    Abstract: P-matrices play a critical role in scientific engineering calculations. Based on Ostrowski-Brauer Sparse (OBS) matrices, a new subclass of P-matrices called Ostrowski-Brauer Sparse B (OBS-B) matrices is introduced, which contains B-matrices and DB-matrices. Moreover, using the infinity norm bound of the inverse of OBS matrices, a computable error bound for the linear complementarity problem of OBS-B matrices is given. And it is shown that the given bound improves the classical bound provided for B-matrices by García-Esnaola and Peña in some cases. Finally, numerical examples are reported to illustrate the effectiveness of the obtained bound.

     

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