On the error in transfinite interpolation by low-rank functions

Nira Dyn, Bert Jüttler*, Dominik Mokriš

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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).

Original languageEnglish
Article number105379
JournalJournal of Approximation Theory
Volume253
DOIs
StatePublished - May 2020

Funding

FundersFunder number
Austrian Science FundNFN S 117

    Keywords

    • Approximation order
    • Low-rank function
    • Transfinite interpolation

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