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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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


Author: 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 $\le n$ in $d$ variables, at a `correct' point set.


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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: http://dx.doi.org/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.
Article copyright: © Copyright 1996 American Mathematical Society