三次样条函数的自动求法

Finding cubic spline interpolating functions automatically

在Matlab的TheSplineToolbox中,没有给出三次样条函数表达式的求法,可在教学过程中,或在实际问题中,我们需要知道样条插值函数的分段表达式。在现行数值分析教材中,一般都是通过解方程确定三次样条插值函数的表达式,但这种方法的工作量很大。在本文中,我们用Matlab语言编制了三个小程序,给出在三种边界条件下,三次样条插值函数表达式的自动求法。

In the Spline Toolbox of Matlab, it does not give the expressions of cubic spline interpolation functions , but we need to know the expressions in teaching process and some practical problems. In most textbooks of numerical analysis, the expressions be got by solving some equations, this method is very troublesome. In this paper, we program three procedures in Matlab language, then we can find cubic spline interpolation functions automatically under three boundary conditions.