离散函数的生成规律及广义GM模型

本文讨论了离散函数曲线的凹向概念及其判定定理;得出“一切正离散函数经过一定阶次的累加生成后必然呈现指数规律”的结论。同时,把文献[1]中的GM模型进行了拓广和论证。

The Generating Rate of Discrete Function and the Generalized GM-Model

Three problems are discussed, namely, (1) The definitions of the cut, the positive discrete function, the curve of discrete function and the concave of a curve of discrete function; the proving of the discriminating rules for the concave of a curve of discrete function;(2)Demonstration of the following theorem: "For any positive discrete function {x(0)(ti)} + , if m(m>1) times of accumulated generating operations are made, then all the curves of the generating function (x(m)(ti)} are of concave-upward and monotone nondecreasing ones; (3) Demonstration of the generalized GM-model, and the conclusion that "To any positive discrete function, the fitting curve can be found by linear differential equation with constant coefficients".