严格双对角占优矩阵行列式的上下界估计  

Estimation of Upper and Lower Bounds for Determinants of Strictly Doubly Diagonally Dominant Matrices

作　　者：段复建[1] 文艳姑 DUAN Fujian;WEN Yangu(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《应用数学》2020年第2期463-474,共12页Mathematica Applicata

基　　金：国家自然科学基金(11461015)。

摘　　要：严格双对角占优矩阵的行列式计算是数值代数中的热点问题.本文首先将严格双对角占优矩阵右乘一个正对角矩阵,使其化为严格对角占优矩阵,其次对严格对角占优矩阵行列式的上下界进行估计,从而得到严格双对角占优矩阵行列式的上下界估计.最后通过数值算例表明所得估计是有效的.The determinant calculation of strictly doubly diagonally dominant matrices is a hot issue in numerical algebra.In this paper,we first multiply the strictly doubly diagonally dominant matrix right by a positive diagonal matrix to make it a strictly diagonally dominant matrix,and then the upper and lower bounds for the determinants of the strictly diagonally dominant matrices are estimated,and the upper and lower bounds for the determinants of the strictly doubly diagonally dominant matrices are obtained.Finally,numerical examples show that the obtained estimates are valid.

关 键 词：对角占优 双对角占优 行列式 界 

分 类 号：O151.21[理学—数学]