摘要
本文针对对角占优矩阵行列式的估计问题,首先利用严格对角占优矩阵A的元素给出逆矩阵A-1的主对角元的上下界,然后利用逐次降阶法及递归给出A的行列式的单调递增的下界序列和单调递减的上界序列,改进了一些已有结果.随后将此方法推广,从而得到对角占优矩阵行列式的上下界序列.最后通过数值算例对理论结果进行验证,数值算例显示所得估计比某些现有估计精确,且在某些情况下能达到真值.
For estimates of the determinant of diagonally dominant matrices, at first, some lower and upper bounds of the main diagonal elements of A^-1 are given using the elements of a strictly diagonally dominant matrix A. And then using successive reduction and recursive methods, monotone increasing sequence of lower bounds and monotone decreasing sequence of upper bounds of determinant of A are given, which improve some existing results and are generalized to obtained sequences of the upper and lower bounds of diagonally dominant matrices. Finally, numerical examples are given to verify the theoretical results and show that the sequence is more accurate than some existing results and can reach the true value of the determinant in some cases.
出处
《应用数学》
CSCD
北大核心
2016年第4期949-955,共7页
Mathematica Applicata
基金
国家自然科学基金(11361074
11501141)
贵州省科学技术基金(黔科合J字[2015]2073号)
贵州民族大学引进人才科研基金(15XRY003)
贵州民族大学科研基金资助项目(15XJS009)
关键词
对角占优
逆
行列式
上下界
序列
Diagonally dominant
Inverse
Determinant
Upper and lower bound
Sequence
作者简介
赵建兴，男，汉族，山东人，副教授，研究方向：数值代数，矩阵理论及其应用．
