On the numerical calculation of topological turning point

Francesco A. Costabile (1) , Francesco Dell'Accio (1) , Luca Guzzardi (1)

1 Dipartimento di Matematica

We introduce the definition of topological turning point of a function $\mathcal{F}(x,\lambda):\mathbb{R}\times\mathbb{R}\rightarrow\mathbb{R}$; then we propose a numerical method for calculating it. This new definition does not require any regularity for $\mathcal{F}$ but its continuity: on the other hand topological turning point coincides with turning point when $\mathcal{F}$ is sufficiently smooth. The numerical method that we introduce has linear speed and it is of secure convergence.

Mots clés: Physical Sciences

Domaines: Informatique [cs]

Francesco A. Costabile, Francesco Dell'Accio, Luca Guzzardi. On the numerical calculation of topological turning point. International Journal of Computer Mathematics, 2011, pp.1. ⟨10.1080/00207160.2011.580342⟩. ⟨hal-00717917⟩