A method for constructing bivariate rational functions by Lagrange weighted interpolation

作者：Jia, Bin^*; Tang, Shuo

来源：Journal of Information and Computational Science, 2011, 8(7): 1155-1163.

• Bivariate
• Bivariate functions
• Continued fraction interpolation
• Data fittings
• Data points
• Inverse differences
• Lagrange
• Lagrange interpolations
• Rational interpolation
• Rectangular grids
• Special forms
• Surface approximation
• Three dimensional space
• Weight functions
• Weighted interpolation

In this paper, a method for constructing rational function by weighted Lagrange interpolation of bivariate function over rectangular grid is discussed, and special form of formula on data points whose abscissas and ordinates are distinct respectively is also given. By this means, problem of branched continued fraction interpolation method (when inverse difference does not exist) can be solved, and on surface approximation and data fitting in three-dimensional space, by properly choosing different weight functions, we can obtain a variety of rational functions, and can reduce the order of the denominator, improve the precision of surface approximation.

• 出版日期2011
• 单位合肥工业大学