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