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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
MathSciNet review:
1344609
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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  in  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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MSC (1991):
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MSC (1991):
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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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