摘要
针对严格α_1-对角占优M-矩阵A的‖A^(-1)‖_∞的估计问题,利用矩阵A的元素和矩阵分裂方法,将矩阵A分裂为严格对角占优M-矩阵B和非负对角矩阵G,进而利用已有严格对角占优M-矩阵的逆矩阵的无穷大范数的上界,给出矩阵B的‖B^(-1)‖_∞的上界Γ(B),此时若Γ(B)与G的最大对角线元的乘积小于1,则可得‖A^(-1)‖_∞的上界.最后通过数值算例对所得结论进行验证,表明所给出的方法可行.
For the estimates of‖A^（-1）‖_∞ of a strictlyα_1-diagonally dominant M-matrix A,the elements of Aand matrix splitting method are used,where Ais expressed as the matrix difference between a strictly diagonally dominant M-matrix Band a nonnegative diagonal matrix G.Using the existing upper bound of infinity norm of the inverse of strictly diagonally dominant M-matrices,the upper boundΓ（B）of‖B^（-1）‖_∞ is obtained.Furthermore,if the product ofΓ（B）and the largest principal diagonal elements of Gis less than 1,then the upper bound of‖A^（-1）‖_∞ is established.Finally,several numerical examples are given to validate the theoretical results,and show that the method in this paper is feasible.
出处
《扬州大学学报（自然科学版）》
CAS
北大核心
2016年第1期1-4,8,共5页
Journal of Yangzhou University：Natural Science Edition
基金
国家自然科学基金资助项目(11361074
11501141)
贵州省科学技术基金资助项目(黔科合J字[2015]2073号)
贵州民族大学引进人才科研基金资助项目(15XRY003)
贵州民族大学科研基金资助项目(15XJS009)
关键词
对角占优
M-矩阵
逆矩阵
范数
上界
diagonally dominant
M-matrix
inverse matrix
norm
upper bound
