Dubuc pioneered a method of interpolation iterative scheme, which is called four-point interpolatory subdivision scheme. Since then, the method has been developed extensively and deeply. However some precise problems proposed by Dubuc are still unsolved after thirty years. In this paper, we will partially solve these problems.

中文翻译：

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关于四点插值细分方案的一些猜想

Dubuc开创了一种插值迭代方案的方法，称为四点插值细分方案。从那时起，该方法得到了广泛而深入的发展。但是，Dubuc提出的一些精确问题在三十年后仍未解决。在本文中，我们将部分解决这些问题。