关键词: 矩形网格, 二元矩阵, 切触有理插值

Abstract: 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.

Key words: rectangular grid, bivariate matrix, osculatory rational interpolation