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Polynomial Ideals, Monomial Bases and a Divided Difference Formula
Pistone, Giovanni
Riccomagno, Eva
Wynn, Henry P.
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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
37 (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.
Languages
en
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