Block Based Bivariate Blending Rational Interpolation via Symmetric Branched Continued Fractions  

作　　者：Qianjin Zhao Jieqing Tan 

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

出　　处：《Numerical Mathematics A Journal of Chinese Universities(English Series)》2007年第1期63-73,共11页

基　　金：Project supported by the National Natural Science Foundation of China (No. 10171026, No. 60473114); the AnhuiProvincial Natural Science Foundation, China (No. 03046102);the Research Funds for Young InnovationGroup, Education Department of Anhui Province (No. 2005TD03).

摘　　要：This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets (blocks). Then construct each block by using symmetric branched continued fraction. Finally assemble these blocks by Newton’s method to shape the whole interpolation scheme. Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton’s polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally, numerical examples are given to show the effectiveness of the proposed method.This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets （blocks）. Then construct each block by using symmetric branched continued fraction. Finally assemble these blocks by Newton＇s method to shape the whole interpolation scheme. Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton＇s polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally, numerical examples are given to show the effectiveness of the proposed method.

关 键 词：插值 函数构造论 二变量 非线性特征 

分 类 号：O174.42[理学—数学]