矩形网格上二元矩阵切触有理插值的新方法

熟知的矩阵切触有理插值的方法都与连分式有关,不仅计算繁琐,而且难以避免出现“极点、不可达点”。用网格点构造有理插值基函数,用型值点构造具有承袭性的各阶矩阵插值算子,通过插值基函数与插值算子作线性运算,构造出二元矩阵各阶切触有理插值函数,有效避免了有理插值的“极点、不可达点”问题。若选择适当的参数,还可以任意降低插值函数的次数,数值例子表明了该方法简单、有效、实用性强。

New method of bivariate matrix osculatory rational interpolation on rectangular grids

The well-known algorithms of the matrix osculatory rational interpolations are all related to continued fractions, continued fraction method not only needs a high computation but also is difficult to avoid "poles and inaccessible points". In this paper, the grid points are applied to construct the rational interpolation base functions, the type value points are applied to construct each order matrix interpolation operators of inheritedness, by interpolation basis functions and interpolation operators do linearity operation, bivariate matrix each order osculatory rational interpolation functions are produced to effectively avoid "poles and inaccessible points" problem of rational interpolation. If the appropriate parameters are selected, it can reduce degree of the interpolation functions arbitrarily, a numerical example shows the method is simple and effective practical.