三次Cardinal样条函数的自由参数优化方案

Free parameter optimization of the cubic Cardinal spline function

为了合理地取定三次Cardinal样条函数所含的自由参数,讨论了插值问题中三次Cardinal样条函数所含自由参数的优化问题。首先分析了自由参数对三次Cardinal样条函数曲线形状的影响,然后给出了数据插值与函数逼近这2种情形下自由参数最优取值的计算方案,分别得到了具有极小二次平均振荡与极小逼近误差的三次Cardinal样条函数。当需要构造具有良好形状保持效果或逼近效果的三次Cardinal样条函数时,可通过所提出的方案选取自由参数的最优取值。

In order to reasonably determine the free parameter of the cubic Cardinal spline function,the optimization of the free parameter of the cubic Cardinal spline function in the interpolation problems are discussed.Firstly,the influence of the free parameter on the curve shape of the cubic Cardinal spline function is analyzed.Secondly,the schemes for computing the optimal free parameter in the two cases of data interpolation and function approximation are given,and the cubic Cardinal spline function with mi-nimal quadratic average oscillation and approximation error are obtained respectively.When it is necessary to construct the cubic Cardinal spline function with good shape preserving effect or approximation effect,the optimal free parameter can be selected by the proposed schemes.