关键词: 二元切触有理插值, 分段组合, 插值公式, 二元埃米特插值

Abstract: The methods of constructing bivariate osculatory rational interpolation function are mostly based on the continued fraction. But feasibility of the algorithm is conditional, the computation is large, and the degree of it is high. It constructs the bivariate osculatory rational interpolation function and extends it to vector-valued case, by means of the method of piecewise combination. It not only solves the existence problem of osculatory rational interpolation function, but also reduces the degree of rational function. Compared to other methods, the course of constructing function is formulary, the degree of rational interpolation function is lower, the feasibility of algorithm is unconditional, and the algorithm needs less computation and facilitates the practical application.

Key words: bivariate osculatory rational interpolation, piecewise combination, interpolation formula, bivariate Hermite interpolation