A continuity property of multivariate Lagrange interpolation
Authors:
Thomas Bloom and JeanPaul Calvi
Journal:
Math. Comp. 66 (1997), 15611577
MSC (1991):
Primary 41A05, 41A63
MathSciNet review:
1422785
Fulltext PDF Free Access
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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 LagrangeHermite 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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 [N]
 G. Nürnberger, Approximation by spline functions, Springer, Berlin, 1989. MR 90j:41025
 [SX]
 T. Sauer and Y. Xu, A case study in multivariate Lagrange interpolation, Approximation Theory, Wavelets and Applications (S. P. Singh, ed.), Kluwer Academic Publishers, 1995, pp. 443452. MR 96d:41036
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 S. Waldron, Integral error formula for the scale of mean value interpolations which includes Kergin and Hakopian interpolation, Numer. Math. (to appear).
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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
JeanPaul Calvi
Affiliation:
Laboratoire de mathématiques, UFR MIG, Université Paul Sabatier, 31062 Toulouse Cedex, France
DOI:
http://dx.doi.org/10.1090/S0025571897008582
PII:
S 00255718(97)008582
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
