A necessary and sufficient condition is derived for the existence of monotone and convex interpolation by a cubic spline with an additional knot inserted between each pair of data points.

本文给出用三次样条在两两节点之间引进一个外加节点的条件下，存在凸而单调的插值的充分必要条件。

youdao

It is acquired from that it makes use of that the interpolation function of cubic spline interpolation has a continuous third derivative on the base of two-dementional cubic convolution interpolation.

它在二维三次卷积插值法的基础上利用三次样条插值法的插值函数具有三阶连续导数的性质而得来的。

youdao

In this paper, we discussed the approximation errors of complex cubic interpolation spline on open smooth curves under the second boundary condition and got the better results.

本文就非闭光滑曲线上关于第二类边界条件的复三次样条函数的逼近误差进行了论讨，取得了较好的结果。

youdao