### New method of bivariate matrix osculatory rational interpolation on rectangular grids

JING Huiqin1, ZHANG Guifang2, LIAO Yongyi1

1. 1.Faculty of Continuing Education, Kunming University of Science and Technology, Kunming 650051, China
2.Faculty of Metallurgy and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, China
• Online:2013-09-01 Published:2013-09-13

### 矩形网格上二元矩阵切触有理插值的新方法

1. 1.昆明理工大学 成人教育学院，昆明 650051
2.昆明理工大学 冶金与能源工程学院，昆明 650093

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.