B-矩阵线性互补问题误差界的新估计式

New Eror Bounds Estimation for the Linear Complementarity Problem of B-matrices

给出了严格对角占优M-矩阵及逆矩阵之间元素的关系式,得到了严格对角占优M-矩阵的逆矩阵的无穷大范数的新上界,结合新界和不等式放缩技巧得到B-矩阵线性互补问题误差界的新估计式,改进了已有的结果.同时,理论证明及数值算例表明了新估计式的有效性.

Some inequalities of element relation on strictly diagonally dominant M-matrix and its inverse matrix are presented,and new upper bounds of the infinity norm of the inverse matrix of strictly diagonally dominant M-matrix are given. The estimations improve the existing results under certain conditions. Combined with the infinite norm for the inverse of strictly diagonally dominant matrix and the range of two important inequalities techniques,a new estimator of the error bound for the linear complementarity problem of B-matrix is obtained. Theoretical analysis and numerical examples show the validity of the new results.