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中文摘要：
Floater和Hormann在2007年给出了重心有理插值的一种新方法,但对于等距节点,插值误差随着d的增大呈现指数级增加。对于这种情况,Klein通过构造扩展的Floater-Hormann插值改善插值效果。文章研究矩形域上的Floater-Hormann重心有理插值的扩展,通过对矩形的两个方向进行延伸,构造了扩展的二元Floater-Hormann重心有理插值,给出的数值实例验证了新方法的有效性。
英文摘要：
In 2007, Floater and Hormann presented a new method of barycentric rational interpolation. However, for equidistant nodes, the interpolation condition deteriorates exponentially with increasing d. In this case,Klein improves this method by extending the Floater-Hormann interpolation under equally spaced node conditions. This paper focuses on the expansion of the Floater-Hormann barycentric interpolation on the rectangular domain. Firstly, the two directions of the rectangle are extended. Then,the extended bivariate Floater-Hormann barycentric rational interpolation is constructed. Finally, an example is given to show the effectiveness of the new method.
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Lebesgue Constant Minimizing Shape Preserving Barycentric Rational Interpolation Optimization algori
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