Worst case and average case cardinality of strictly acute stencils for two dimensional anisotropic fast marching

Jean-Marie Mirebeau (1, 2) , François Desquilbet (3)

1 CNRS - Centre National de la Recherche Scientifique
2 LMO - Laboratoire de Mathématiques d'Orsay
3 ENS-PSL - École normale supérieure - Paris

We study a one dimensional approximation-like problem arising in the discretization of a class of Partial Differential Equations, providing worst case and average case complexity results. The analysis is based on the Stern-Brocot tree of rationals, and on a non-Euclidean notion of angles. The presented results generalize and improve on earlier work.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Jean-Marie Mirebeau, François Desquilbet. Worst case and average case cardinality of strictly acute stencils for two dimensional anisotropic fast marching. CONSTRUCTIVE THEORY OF FUNCTIONS, Jun 2019, Sozopol, Bulgaria. ⟨hal-02316311⟩