A continuity property

of multivariate Lagrange interpolation

Authors:
Thomas Bloom and Jean-Paul Calvi

Journal:
Math. Comp. **66** (1997), 1561-1577

MSC (1991):
Primary 41A05, 41A63

DOI:
https://doi.org/10.1090/S0025-5718-97-00858-2

MathSciNet review:
1422785

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a sequence of interpolation schemes in of degree (i.e. for each one has unique interpolation by a polynomial of total degree and total order . Suppose that the points of tend to as and the Lagrange-Hermite interpolants, , satisfy for all monomials with . **Theorem**: for all functions of class in a neighborhood of . (Here denotes the Taylor series of at 0 to order .) Specific examples are given to show the optimality of this result.

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Additional Information

**Thomas Bloom**

Affiliation:
Department of Mathematics, University of Toronto, M5S 1A1, Toronto, Ontario, Canada

Email:
bloom@math.toronto.edu

**Jean-Paul Calvi**

Affiliation:
Laboratoire de mathématiques, UFR MIG, Université Paul Sabatier, 31062 Toulouse Cedex, France

DOI:
https://doi.org/10.1090/S0025-5718-97-00858-2

Keywords:
Multivariable Lagrange interpolants,
interpolation schemes in ${\mathbb{R}}^{n}$,
Kergin interpolation

Received by editor(s):
January 30, 1996

Received by editor(s) in revised form:
August 21, 1996

Additional Notes:
The first author was supported by NSERC of Canada.

Article copyright:
© Copyright 1997
American Mathematical Society