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http://hdl.handle.net/10077/4145| Title: | Polynomial Ideals, Monomial Bases and a Divided Difference Formula | Authors: | Pistone, Giovanni Riccomagno, Eva Wynn, Henry P. |
Keywords: | Divided differences; Polynomial ideals; Taylor approximation | Issue Date: | 2005 | Publisher: | Università degli Studi di Trieste. Dipartimento di Matematica e Informatica | Source: | G. Pistone, E. Riccomagno, H.P. Wynn, "Polynomial Ideals, Monomial Bases and a Divided Difference Formula", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 37 (2005), pp. 121-144. | Series/Report no.: | Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics 37 (2005) |
Abstract: | A generalised (multivariate) divided difference formula is given for an arbitrary finite set of points with no subsets of three points that lie on a line. This follows from an extension of the Newton’s polynomials and Newton’s interpolation formula. It is derived as the interpolation based on Gr¨obner bases for the grid expressed as a zero-dimensional variety and is typically dependent on the chosen term-ordering and the selected ordering of points in the grid. |
Type: | Article | URI: | http://hdl.handle.net/10077/4145 | ISSN: | 0049-4704 |
| Appears in Collections: | Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.37 (2005) |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| PistoneRiccomagnoWynnRendMat37.pdf | 187.42 kB | Adobe PDF |  View/Open |
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