Research On The Existence Of Rational Interpolation Function

On the research of rational approximation, it is very important to determine the existence of rational interpolation function. This thesis gives the existence criterion of osculating rational interpolation and bivariate rational interpolation .It is composed of four chapters.In the first chapter, we outline the background and the main results obtained in this thesis.In the second chapter, we first state some basic concepts and theorem, then we introduce two ways determine the existence of Rational Interpolation using Lagrange interpolation formula and Newton interpolation formula. Finally, we compare the two different ways.In the third chapter, by means of the generalized Vandermonde determinant's application in Hermite interpolation, we set up another existence criterion of osculating rational interpolation;this criterion is easier to be mastered and to be understanded than existing ones.In the forth chapter, we first give the existence criterion of bivariate rational interpolation and its representation formula using overlay algorithm, then we introduce the existence criterion with Lagrange interpolation function. By comparing them, we arrive at a conclusion that the way given in this chapter is more flexible.