TY - JOUR
T1 - On the error in transfinite interpolation by low-rank functions
AU - Dyn, Nira
AU - Jüttler, Bert
AU - Mokriš, Dominik
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/5
Y1 - 2020/5
N2 - 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).
AB - 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).
KW - Approximation order
KW - Low-rank function
KW - Transfinite interpolation
UR - http://www.scopus.com/inward/record.url?scp=85079551045&partnerID=8YFLogxK
U2 - 10.1016/j.jat.2020.105379
DO - 10.1016/j.jat.2020.105379
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AN - SCOPUS:85079551045
SN - 0021-9045
VL - 253
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
M1 - 105379
ER -