Convergence of multivariate polynomials interpolating on a triangular array

Authors:
T. N. T. Goodman and A. Sharma

Journal:
Trans. Amer. Math. Soc. **285** (1984), 141-157

MSC:
Primary 41A05; Secondary 30E05

MathSciNet review:
748835

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Abstract: Given a triangular array of complex numbers, it is well known that for any function smooth enough, there is a unique polynomial of degree such that on each of the first rows of the array the divided difference of coincides with that of . This result has recently been generalized to give a unique polynomial in variables of total degree which interpolates a given function on a triangular array in . In this paper we extend some results of A. O. Gelfond and derive formulas for and to prove some results on convergence of to as under various conditions on and on the triangular array.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0748835-5

Keywords:
Kergin interpolation,
multivariate approximation,
divided difference

Article copyright:
© Copyright 1984
American Mathematical Society