分形、神经网络、细胞自动机原理及其插值方法研究

Study on theories of fractal, nerve net, cellular automaton and interpolation method

传统的插值方法存在许多不足之处。将分形、神经网络、细胞自动机等非线性科学理论与传统的插值方法相结合,解决了传统的插值方法所不能解决的问题。分形插值使相邻两插值点之间的局部变化特征得以描述;人工神经网络插值解决了机理尚不明确的问题;基于细胞自动机理论的曲面重构使得整张拟合曲面的光顺性得到保证。文中对这些非线性插值方法逐一进行探讨。

There is a great number of shortcomings in the traditional interpolation method. The (combination) of nonlinear scientific theories of fractal, nerve net, cellular automaton etc with the traditional interpolation method has solved the problem that can't be settled by the traditional interpolation method. The character of point-to-point local change can be described by the method of fractal interpolation. The problem which modeling isn't definite can be settled by the method of nerve net interpolation. The smoothness of curved face can be held by the surface fitting method based on the theory of cellular (automaton). The nonlinear interpolation method is discussed in this paper.