再谈广义Z-矩阵及广义M-矩阵的若干性质

Once More Discussion for the Properties of Generalized Z - Matrices andGeneralized M - Matrices

给出了广义线性互补问题中常用到的广义Z-矩阵及广义M矩阵的若干性质。这些性质主要遗传于通常意义下的Z-矩阵及M-矩阵的性质。根据矩阵论的有关知识,已经知道Z-矩阵及M-矩阵有很多良好的性质,尤其是M-矩阵的等价命题已经研究出几十种。从这些性质中受到启发,得到了广义Z-矩阵及广义M-矩阵与其类似的若干结论,这将为更好的求解广义线性互补问题奠定基础。同时,也会给其他相关领域得到应用,如偏微分方程的有限差分法和有限元素法、经济学中的投入产出、概率统计中的Markov过程等。

Some properties of generalized Z - matrices and M - matrices were given for solving the generalized linear complementarity problem. These properties are mainly inherited from the properties of Z - matrices and M - matrices in common meaning. According to knowledge of matrice theory, it is known that Z - matrices and M - matrices have many properties, especially tens of equal conclusions about M - matrices. Get some conclusions of generalized Z - matrices and M - matrices like them, and it must provide strong base for solving the generalized linear complementarity problems, meanwhile, it will also make the future of irrelative fields(such as finite difference method and finite element methods of partial differential equation/input - output method of economic and so on) more prospective.