Polynomials with bounds and numerical approximation

Bruno Després (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We discuss the generation of polynomials with two bounds-an upper bound and a lower bound-on compact sets in various dimensions. We show that a composition formula based on a weighted 4-squares Euler identity generates all such polynomials in dimension d = 1. Higher dimensions are discussed by means of the 8-squares Degen identity and tensorization, and the connection with quaternions algebras is made explicit. Various numerical results illustrate the potentialities of this approach and some implementation details are provided.

Mots clés: polynomials with bounds; 4-square Euler identity; Polynomial Algorithm

Domaines: Analyse numérique [math.NA]

Bruno Després. Polynomials with bounds and numerical approximation. Numerical Algorithms, 2017. ⟨hal-01307999v3⟩