Some Research About Rational Interpolation Method

Rational interpolation is a famous applied interpolation method on the aspectof function approaching, which is wide spread on the domain of computer Graphicsand applied mathematic approach and so on. Some research about rationalinterpolation method has been studied very thorough. First of all, we introducedLagrange-Thiele-like rational interpolation method and a kind of bivariateBarycentric rational interpolating method in this paper. The Lagrange-Thiele-likerational interpolation method provides various flexible forms about rationalinterpolation method. Univariate Lagrange polynomial interpolation is a kind ofunivariate Barycentric rational interpolation. Based on the expansion of thedeformation of univariate Lagrange polynomial interpolation function, we get thebivariate Barycentric rational interpolating method. This method not onlyovercomes a lot of shortcomings compared with bivariate Lagrange interpolatingmethod, such as a great deal of calculation, numerical instability and so on. It butalso inherits some advantages of the Barycentric rational interpolating method,such as: a small amount of calculation, numerical stability and easy to control theappearance of poles and unattainable points and so on. The existing problem of anyrational interpolation is the primary consideration for theoretic and practicalapplications. In This paper, on the base of plenty of references, provides a note onthe Neville-like rational interpolating method, in order to solve the problem offorming unsatisfied interpolating functions, which have unattainable interpolationpoles. Then we give the error comparison, and at the end of this paper we finallyprovide a numerical example to confirm the feasibility and the accuracy of this newalgorithm.