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On the error in transfinite interpolation by low-rank functions
Journal of Approximation Theory ( IF 0.9 ) Pub Date : 2020-02-06 , DOI: 10.1016/j.jat.2020.105379
Nira Dyn , Bert Jüttler , Dominik Mokriš

Given a bivariate function and a finite rectangular grid, we perform transfinite interpolation at all the points on the grid lines. By noting the uniqueness of interpolation by rank-n functions, we prove that the result is identical to the output of Schneider’s CA2D algorithm (Schneider, 2010) . Furthermore, we use the tensor-product version of bivariate divided differences to derive a new error bound that establishes the same approximation order as the one observed for n-fold transfinite interpolation with blending functions (Gordon and Hall, 1973).



中文翻译:

低阶函数在超限插补中的误差

给定一个双变量函数和一个有限的矩形网格,我们在网格线上的所有点上执行超限插值。通过注意按等级进行插值的唯一性-ñ函数,我们证明结果与Schneider的CA2D算法的输出相同(Schneider,2010年)。此外,我们使用二元除法差的张量积形式来推导一个新的误差界限,该误差界限与观察到的误差界限建立了近似的阶数。ñ混合函数的多重折叠超限内插(Gordon and Hall,1973)。

更新日期:2020-02-06
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