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。
Then the accuracy of approximation, regularity of many-knot splines interpolation method and frequency property of the interpolation kernel are worked out for comparison.
然后分析了多结点样条插值方法的逼近精度、正则性、插值核函数的频域特性。
New results are: present new expression for the basic function of many knot spline interpolation;
主要的新结果是：对多结点样条基本函数的构造给出了新的表述；
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