Estimations for Determinats of Dashnic-Zusmanovich Type Matrices  

Dashnic-Zusmanovich型矩阵的行列式估计

作　　者：Liu Dan Wang Shiyun Zhou Lixin Lyu Zhenhua 刘丹;王诗云;周立新;吕振华(沈阳航空航天大学理学院,沈阳110136;桂林航空工业学院理学院,桂林541199)

机构地区：[1]School of Science,Shenyang Aerospace University,Shenyang 110136,China [2]School of Science,Guilin University of Aerospace Technology,Guilin 541199,China

出　　处：《数学理论与应用》2024年第4期116-126,共11页Mathematical Theory and Applications

基　　金：supported by the National Natural Science Foundation of China(No.12171323);the Natural Science Foundation of Guangxi Province(No.2023GXNSFAA026514)。

摘　　要：To estimate the determinant of a matrix is a hot issue in numerical algebra.The class of H-matrices has a wide range of applications in many fields such as computational mathematics,control theory.In this paper,the estimations for determinants of Dashnic-Zusmanovich type matrices are studied.For a Dashnic-Zusmanovich type matrix,we transform it into a diagonally dominant matrix by using scaling matrices.Then we obtain the upper and lower bounds for the determinant of the Dashnic-Zusmanovich type matrix.Numerical examples are given to illustrate the effectiveness of the proposed results.矩阵的行列式估计是数值代数中的热点问题.H-矩阵在数学物理、控制论等许多领域有着重要的研究价值.本文研究H-矩阵的一个子类Dashnic-Zusmanovich型矩阵的行列式估计问题.我们通过把Dashnic-Zusmanovich型矩阵转化为对角占优矩阵,得到Dashnic-Zusmanovich型矩阵行列式的上下界估计.数值算例说明了本文结果的有效性.

关 键 词：Nonsingular H-matrix Dashnic-Zusmanovich type matrix DETERMINANT 

分 类 号：O15[理学—数学]