一种新的二元有理插值及其性质

构造了一种带参数的仅基于函数值的分子为双四次、分母为双二次的二元有理插值样条函数,插值函数具有简洁的显式表示。插值函数中含有4个参数,当这些参数满足一定条件时,插值曲面在插值区域上C1光滑。由于插值函数中含有参数,这样可以在插值数据不变的情况下通过对参数的选择进行插值曲面的局部修改。最后讨论了插值函数的一些性质。

A New Bivariate Rational Interpolation and the Properties

A bivariate rational biquartic interpolating spline based on function values with four parameters is constructed, and this spline is with biquartic numerator and biquadratic denominator. The interpolating function has a simple and explicit mathematical representation, which is convenient both in practical application and in theoretical study. The interpolating surface is C1 in the interpolating region when two of the parameters satisfiy a simple condition, when another two parameters are selected suitably, the interpolating function could be expressed in matrix form. The interpolating surface can be modified by selecting suitable parameters under the condition that the interpolating data are not changed. Some properties of the interpolation are derived.