三次样条插值函数的构造与Matlab实现

三次样条插值函数边界条件由实际问题对三次样条插值在端点的状态要求给出.以第1边界条件为例,用节点处二阶导数表示三次样条插值函数,用追赶法求解相关方程组.通过Matlab编制三次样条函数的通用程序,可直接显示各区间段三次样条函数体表达式,计算出已给点插值并显示各区间分段曲线图.

Construction and Realization of Cubic Spline Interpolation Function

The boundary conditions of cubic spline were given by the practical state at the extreme points of discrete function. Taking the first boundary condition as an example, it used the second order derivative of the junctions to represent the cubic spline interpolation function, and solved the relative equations with chasing method. The universal procedure of cubic spline was realized under the environment of Matlab, which could compute the interpolation point and directly display the exact expression of function and segmental curve in each interval.