Abstract The histopolation with quadratic/linear rational splines of class C 2 is studied. These splines keep the sign of its second derivative on the whole interval and because of that the given histogram is assumed to be strictly convex. The grid points of the histogram and spline knots between them are supposed to be placed arbitrarily. We show that there is a strictly convex histogram without the solution of histopolation problem for any choice of spline knots. Presented numerical examples illustrate this result.

中文翻译：

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凸数据的有理样条直方插值

摘要 研究了C 2 类二次/线性有理样条的直方插值。这些样条在整个区间上保持其二阶导数的符号，因此假定给定的直方图是严格凸的。直方图的网格点和它们之间的样条结点应该是任意放置的。我们表明，对于任何样条结的选择，都有一个严格凸直方图，而没有直方插值问题的解决方案。给出的数值例子说明了这个结果。