海洋资料整理中一种单调分段插值方法的应用

Abstract

以三次HErMITE插值函数和另二类初等形式的函数为基础所构造的一种混合型分段插值函数进行海洋资料整理中的插值和绘线处理，结果更加合理。特别对具有累加或统计性质的数据，不但给出光滑的插值函数及其图形，而且还能给出大部分光滑的导函数图形。本文同时介绍了上述方法在不同专业领域中的一些应用实例。

A sort of multicmponent picewise interpolatin Function, which is compsed of the cubic Hermite Interpolation Functin and tw other sorts of the elementary Functions, possesses the properties as the Following: 1.montonicity in the whle interval [a,b ]; 2.continuous second derivative in thse subintervals (esp.at the knts) in which the Cubic Spline Function can be assigned to be the interpolatin Function ; 3.continuous First derivative at the rest knots.The application F this sort of interpolation Function is intrduced in this paper, with its satisFied perFrmance.Especially, For the data with the characteristics of statistics and cumulation, not only a mnotone and smooth interpolation Function and its curve can be derived by this method, but als a smooth derivative Function and its curve in most subintervals of the interval [a, b], by means of cmputer.Several examples of the application of this method in data processing in diFFerent disciplines of the marine sciences are illustrated.