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Necessary and sufficient conditions for almost regularity of uniform Birkfoff interpolation schemes. (English) Zbl 1101.41002

Summary: In this article, using a combination of the necessary and sufficient conditions for almost regularity of an interpolation scheme, we will determine all plane uniform Birkhoff scheme, when the set of interpolated node has \(n\) elements and the set of derivatives we are interpolating with is \(A=\{(0,0),(1,0)\}\).
For the same \(A\) we will determine all rectangular Birkhoff uniform interpolation schemes (the set of nodes has rectangular shape) and we will take not of the fact that these two results differ significantly.

MSC:

41A05 Interpolation in approximation theory
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