Study On The Existence Of Rational Interpolation

This thesis consists of three parts. The first part reviews the evolution of the study for existence of rational interpolation.The second part studies the relationship between the existence of a rational interpolant and the place of the interpolating data points through which the interplant passed:For given m+2 data points, we give a method to ensure the existence of a rational interpolant of [m/1] type by analyzing the placement of the data points, and then present the corresponding expression of the rational interpolant. Some numerical examples illustrate the technique.The third part gives a method to test the existence of a class of bivariate rational interpolants by using of bivariate Lagrange interpolation, and presents the relevant expressions of the interpolants if they are existent. In addition, we offer a method to solve the problem of unattainable points of the bivariate rational interpolation which may convert unattainable points into attainable points. Numerical examples show the feasibility of the method.