The Limiting Case of Blending Differences for Bivariate Blending Continued Fraction Expansions  

作　　者：赵前进 檀结庆 

机构地区：[1]School of Computer & Information,Hefei University of Technology,Hefei,230009 [2]Institute of Applied Mathematics,Hefei University of Technology,Hefei,230009

出　　处：《Northeastern Mathematical Journal》2006年第4期404-414,共11页东北数学（英文版）

基　　金：The NNSF(10171026 and 60473114)of China;the Research Funds(2005TD03) for Young Innovation Group,Education Department of Anhui Province.

摘　　要：For a univariate function given by its Taylor series expansion, a continued fraction expansion can be obtained with the Viscovatov＇s algorithm, as the limiting value of a Thiele interpolating continued fraction or by means of the determinantal formulas for inverse and reciprocal differences with coincident data points. In this paper, both Viscovatov-like algorithms and Taylor-like expansions are incorporated to yield bivariate blending continued expansions which are computed as the limiting value of bivariate blending rational interpolants, which are constructed based on symmetric blending differences. Numerical examples are given to show the effectiveness of our methods.For a univariate function given by its Taylor series expansion, a continued fraction expansion can be obtained with the Viscovatov＇s algorithm, as the limiting value of a Thiele interpolating continued fraction or by means of the determinantal formulas for inverse and reciprocal differences with coincident data points. In this paper, both Viscovatov-like algorithms and Taylor-like expansions are incorporated to yield bivariate blending continued expansions which are computed as the limiting value of bivariate blending rational interpolants, which are constructed based on symmetric blending differences. Numerical examples are given to show the effectiveness of our methods.

关 键 词：INTERPOLATION continued fractions symmetric blending differences expansion 

分 类 号：O241.3[理学—计算数学]