The numerical calculation of topological turning points

Abstract

We introduce the definition of topological turning point of a function ℱ(x, λ): ℝ×ℝ→ℝ, then we propose a numerical method for calculating it. This new definition does not require any regularity for ℱ but its continuity; moreover, topological turning point coincides with turning point when ℱ is sufficiently smooth. The numerical method that we introduce has linear rate of convergence, and it is of secure convergence.

Keywords:

• critical point
• turning point
• direct method

2000 AMS Subject Classifications :

• Primary: 58K05
• Secondary: 65H10