单边无限区间上五次样条插值的渐近展式及叠样条逼近

The Term by Term Expansions for Quintic Interpolating Splines in [0,+∞) and the Spline on spline Approximation

给出了单边无限区间上一类重要高次插值样条——五次样条函数的逐项渐近展式．利用它可得到超收敛结果和进行外推等工作．另外还给出了一种高精度逼近导函数的方法．

In this paper, we obtain the term by term expansions for quintic spline interpolating function defined in [0,+∞). Based on it, we give the super convergence in the knots and can carry out extrapolation works etc. In addition, the spline on spline approximation of the derivative is obtained.