中文摘要：

本文讨论了三次样条插值函数(cubic spline)边界条件的更一般情形。将边界条件的"端点"导数条件换成"中间插值节点"的导数,从而将求样条函数的"三对角矩阵"进行了降阶并向"上(下)三角矩阵"的转化。在理论上证明了新边界条件下样条函数构造的唯一性,并通过数值实验验证了新边界条件下的样条函数与元函数有较好地拟合度。

英文摘要：

This paper generalizes the boundary conditions of cubic spline interpolation.The author changes the derivative boundary conditions from extreme points to intermediate interpoltation nodes.Then,the primary tridiagonal matrix is turned to be lower triangular matrixes and upper(or lower)triangular matrixes.The author proves the existence and uniqueness of the new spline interpolation in theory,and verifies the spline function with new boundary conditions has a better fitting with the primary function by some numerical experiments.