区域函数

Function of Region

摘要: 为了把点函数理论、区间函数理论和方法推广到任意区域,作者建立了区域的收缩和区域的保核收缩,区域的扩张和区域的保核扩张等新理论.从这些概念出发,给出了区域函数的新定义,并将区域函数的核(即不动点)与此区域函数的定义区域的稳定中心联系起来,从而建立了区域理论,和区域与区域算法. 在应用中,为了求区域的稳定中心,作者采用了由Hartfiel和其它作者建立的矩阵测度理论;并讨论了与区域相伴的线性代数方程组系数矩阵的测度理论.

Abstract: The purpose of this paper is to extend points function and interval functions theoretics to an arbitrary region. For this, the new theory, the contraction of a region, and the retraction of a region; the extension of a region, and the kernel-preserving extension of a region are established by the author. Starting from these concepts, the new definitions of a region function is given. And a kernel(i.e. fixed point) of a region function is connected with a stable centre of defining region of such a region function. Thereby, the region theoretics and algorithms are established.In applications, to find a stable centre of a region, the author has utilized the measure theoretics of matrice defined by Hartfiel[7] and other authors. The measure problems of coefficient matrice of system of equations of linear algebra associated with some region are discussed.

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