Algorithm Research Of Bivariate Rational Interpolation Based On Continued Fraction

Continued fraction interpolation is a nonlinear interpolation,It is not only have been widely used in the numerical integration, numerical solution of differential equations, integral calculation, integral equations, special functions of mathematical physics in the asymptotic expansion, number theory, Markov process theory, moment problems and death process, chaos, theoretical physics and other fields ,But also in control theory, statistical mechanics, mechanical vibration, mode analysis, signal processing and other engineering technologies have significant applications .This paper chiefly discusses the algorithm problem of bivariate rational interpolation based on continued fraction ,the algorithm described here include recursive algorithm and matrix algorithm, the main content inclueds bivariate Newton-Thiele–like blending continued fraction interpolation algorithm,Thiele-Newton-like blending continued fraction interpolation algorithm, It is not difficult to find that, these types of rational interpolation are generated in one way or another by interpolation of unvariate Newton-like polynomials and unvaraite Thiele-like continued fraction interpolation. Several bivariate interpolation format can be expresses in a unified framework ,Teacher Jie-Qing Tan gives the general framework of bivariate rational interpolation based on continued fraction,this paper gives the corresponding matrix algorithm. In this paper, a new bivariate continued fraction interpolation is constructed by the Newton interpolation polynomial interpolation and associated continued fraction interpolation, at the same time, we also give a new equivalent method - matrix algorithm, numerical examples show the effectiveness of the algorithm.