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A canonical form for the continuous piecewise polynomial functions

Abstract: We present in this paper a canonical form for the elements in the ring of continuous piecewise polynomial functions. This new representation is based on the use of a particular class of functions {Ci(P) : P ? Q[x], i = 0, . . . , deg(P)} defined by Ci(P)(x) = ? 0 if x ? ? P(x) if x ? ? where ? is the ith real root of the polynomial P. These functions will allow us to represent and manipulate easily every continuous piecewise polynomial function through the use of the corresponding canonical form. It will be also shown how to produce a ??rational?? representation of each function Ci(P) allowing its evaluation by performing only operations in Q and avoiding the use of any real algebraic number.

 Fuente: Journal of Computational and Applied Mathematics 283 (2015) 17?27

Editorial: Elsevier

 Año de publicación: 2015

Nº de páginas: 10

Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.cam.2014.11.033

ISSN: 0377-0427,1879-1778

Proyecto español: MTM2011-25816-C02-02

Url de la publicación: https://doi.org/10.1016/j.cam.2014.11.033