%0 Journal Article
%T 非奇异<i>H</i>-矩阵的迭代判别新条件<br>New Conditions for Iterative Discrimination of Nonsingular <i>H</i>-Matrices
%A 谢智慧
%A 陈茜
%J Advances in Applied Mathematics
%P 208-217
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.145249
%X 非奇异<i>H</i>-矩阵是一类应用广泛的特殊矩阵&#65292;在矩阵理论、控制论和神经网络等许多领域有重要的应用。本文利用矩阵的相关性质&#65292;通过对非占优行指标集进行细分和构造新迭代因子的方法&#65292;得到新正对角因子&#65292;提出一组具有迭代形式的非奇异<i>H</i>-矩阵判定的新条件&#65292;并相应给出了非奇异<i>H</i>-矩阵迭代判定算法&#65292;最后利用数值实例验证了算法的有效性。<br>Nonsingular <i>H</i>-matrices are a kind of special matrices with wide applications in many fields such as matrix theory, control theory and neural networks. In this paper, by using the relevant properties of matrices and through the method of subdividing the set of non-dominant row indices and constructing new iterative factors, a new positive diagonal factor is obtained. A new set of conditions for determining nonsingular <i>H</i>-matrices in iterative form is presented, and the corresponding iterative discrimination algorithm for nonsingular <i>H</i>-matrices is given. The effectiveness of the algorithm is verified by numerical examples.
%K 非奇异<i>H</i>-矩阵&#65292
%K 迭代算法&#65292
%K 不可约&#65292
%K 非零元素链<br>Nonsingular <i>H</i>-Matrix
%K Iterative Algorithm
%K Irreducible
%K Nonzero Elements Chain
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=114800