Pré-Publication, Document De Travail Année : 2016

Polynomials with bounds and numerical approximation

Bruno Després

Résumé

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.

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Dates et versions

hal-01307999 , version 1 (27-04-2016)
hal-01307999 , version 2 (11-05-2016)
hal-01307999 , version 3 (26-09-2016)

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  • HAL Id : hal-01307999 , version 2

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Bruno Després. Polynomials with bounds and numerical approximation. 2016. ⟨hal-01307999v2⟩
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