On the Sauer-Xu formula for the error in multivariate polynomial interpolation
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- by Carl de Boor PDF
- Math. Comp. 65 (1996), 1231-1234 Request permission
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
- Carl de Boor, A multivariate divided difference, Approximation Theory VIII, Academic Press, New York, 1995, pp. 87–96.
- Charles A. Micchelli, On a numerically efficient method for computing multivariate $B$-splines, Multivariate approximation theory (Proc. Conf., Math. Res. Inst., Oberwolfach, 1979) Internat. Ser. Numer. Math., vol. 51, Birkhäuser, Basel-Boston, Mass., 1979, pp. 211–248. MR 560673
- Thomas Sauer and Yuan Xu, On multivariate Lagrange interpolation, Math. Comp. 64 (1995), no. 211, 1147–1170. MR 1297477, DOI 10.1090/S0025-5718-1995-1297477-5
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
- 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 1996 American Mathematical Society
- Journal: Math. Comp. 65 (1996), 1231-1234
- MSC (1991): Primary 41A05, 41A10, 65D05
- DOI: https://doi.org/10.1090/S0025-5718-96-00727-2
- MathSciNet review: 1344609