On The Methods Of Constructing Osculatory Rational Interpolating Function

Existing methods of constructing oscillatory rational interpolating function are almost related to calculation of continued fractions. So the feasibility of their algorithms is conditional and they need a large amount of calculation. For assigned interpolating condition, whether we can construct osculatory rational interpolating function just like constructing multinomial interpolating function is worth researching. In this paper we introduce interpolating operator of polynomial form and parameters which is fixed to treat, and construct osculatory rational interpolating function by the method of convex combination. For osculatory rational interpolating function that we have constructed,we can reduce its number of times by choosing parameters. This method of constructing osculatory rational interpolating function is easy. The calculating course is formulism and convenient to be realized on the computer. It needs a small amount of calculation. So it has immense application foreground.Main contents of this thesis are listed as follows: At first, we detailedly introduce some basic concepts and properties of osculatory rational interpolation, and existing methods of constructing osculatory rational interpolating function. We discuss with emphasis constructing osculatory rational interpolating function (or vector-valued osculatory rational interpolating function, matrix-valued osculatory rational interpolating function) by the method of convex combination, and we also discuss the method of reducing number of times of rational fraction. Then we popularize this method of constructing osculatory rational interpolating function to bivariate osculatory rational interpolation. At last, we have discussion about existence of biariate osculatory rational interpolation and produce its explicit expression.