On the error in transfinite interpolation by low-rank functions

Abstract

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).