Some Researches On Construction Methods Of Rational Interpolants Function

Rational fraction function is more complicated than the polynomial, but it ismore flexible and effective than the polynomial function. Thus the rationalinterpolation problem has been subject to attention. As how to construct rationalfunction we have got some great progress by the efforts of the schools all over theworld. This paper laid foundation on the existing research, we constructed two newformula of interpolation combined the barycentric rational interpolation, continuedfraction interpolation and polynomial interpolation. The special arrangements areas follows:In chapter1, it introduces the research introduction and development processof the rational interpolation, the work to be done in the paper.In chapter2, it briefly introduces the basic theory and methods of the rationalinterpolation.In chapter3, Firstly, new blending rational interpolants are constructed basedon Thiele-type continued fraction interpolants and Barycentric rational interpolants.Secondly, the bivariate rational interpolations have no poles was proved. Thereforeit is now quite easy to check that the bivariate rational interpolations caninterpolate the original function at these points. At the same time, based on theproperty of the Newton interpolation, the approximation error of the barycentricbivariate rational interpolations was analyzed. Lastly, numerical example andgraphics are given to show the correctness and effectiveness of the new method.In chapter4, an efficient method for interpolation with stationary points isPresented based on divided differences algorithm and Lagrange algorithm, it isshown that the suggested method is more efficient. The derivatives of theInterpolation functions at interpolation knot are also zeros. Thus we get theinterpolation with stationary points effectively.In chapter5, for the questions which were to be researched, it gives briefsummary and presents some questions which are worthwhile to explore andresearch.