基于α-链对角占优H-矩阵的判定

Criteria for H-Matrices Based on α-Chain Diagonally Dominant

H-矩阵是数学和工程应用中的一类特殊矩阵,它在数值代数、数学物理、控制理论等领域有着重要的应用。根据α-链对角占优的性质,通过构造正对角矩阵以及分割矩阵指标集,运用加权平均不等式、不等式放缩等技巧,得到了判别非奇异H-矩阵的充分条件。最后,通过数值实例来说明判定方法的有效性。

As a special class of matrix in the mathematical and engineering applications,H-matrix also finds its important application in the fields of numerical algebra,mathematical physics,control theory,etc.Based on the properties ofα-chain diagonally dominant,sufficient conditions for the discrimination of the non-singular H-matrix has thus been obtained by constructing the positive diagonal matrix and the index set of partition matrix,and by adopting such techniques as the weighted mean inequality and inequality zooming.Finally,corresponding numerical examples are presented to verify the validity of the determination method.