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On the Sauer-Xu formula for the error in multivariate polynomial interpolation

Author(s): Carl de Boor.
Journal: Math. Comp. 65 (1996), 1231-1234.
MSC (1991): Primary 41A05, 41A10, 65D05
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Abstract: Use of a new notion of multivariate divided difference leads to a short proof of a formula by Sauer and Xu for the error in interpolation, by polynomials of total degree $\le n$ in $d$ variables, at a `correct' point set.

References:

1.: Carl de Boor, A multivariate divided difference, Approximation Theory VIII, Academic Press, New York, 1995, pp. 87--96.
2.: C. A.Micchelli, On a numerically efficient method for computing multivariate B-splines, Multivariate Approximation Theory, Birkhäuser, Basel, 1979, pp. 211--248. MR 81g:65017
3.: T.Sauer and Yuan Xu, On multivariate Lagrange interpolation, Math. Comp. 64 (1995), 1147--1170. MR 95j:41051

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Additional Information:

Carl de Boor
Affiliation: Computer Sciences Department, University of Wisconsin-Madison, 1210 W. Dayton St., Madison, Wisconsin 53706
Email: deboor@cs.wisc.edu

DOI: 10.1090/S0025-5718-96-00727-2
PII: S 0025-5718(96)00727-2
Keywords: Polynomials, multivariate, interpolation, error, remainder formula, divided difference
Received by editor(s): May 8, 1995
Additional Notes: This work was supported by the NSF grant DMS-9224748, by the US-Israel Binational Science Foundation under Grant No. 90-00220, and by ARO under Grant No. DAA H04-95-1-0089.
Copyright of article: Copyright 1996, American Mathematical Society


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