We introduce the definition of topological turning point of a function ${\mathcal F}(x, λ):{\mathbb R}\times{\mathbb R}\mapsto {\mathbb R}$, then we propose a numerical method for calculating it. This new definition does not require any regularity for ${\mathcal F}$ but its continuity; moreover, topological turning point coincides with turning point when ${\mathcal F}$ is sufficiently smooth. The numerical method that we introduce has linear rate of convergence, and it is of secure convergence.
The numerical calculation of topological turning points
DELL'ACCIO, Francesco;
2011-01-01
Abstract
We introduce the definition of topological turning point of a function ${\mathcal F}(x, λ):{\mathbb R}\times{\mathbb R}\mapsto {\mathbb R}$, then we propose a numerical method for calculating it. This new definition does not require any regularity for ${\mathcal F}$ but its continuity; moreover, topological turning point coincides with turning point when ${\mathcal F}$ is sufficiently smooth. The numerical method that we introduce has linear rate of convergence, and it is of secure convergence.File in questo prodotto:
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