Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4639069 | Journal of Computational and Applied Mathematics | 2014 | 18 Pages |
Abstract
This paper investigates the sufficient conditions for the asymptotic convergence of a generic branch and prune algorithm dedicated to the verified quadrature of a function in several variables. Quadrature over domains defined by inequalities, and adaptive meshing strategies are in the scope of this analysis. The framework is instantiated using certified quadrature methods based on Taylor models (i.e. Taylor approximations with rigorously bounded remainder), and reported experiments confirmed the analysis. They also show that the performances of the instantiated algorithm are comparable with current methods for certified quadrature.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Alexandre Goldsztejn, Jorge Cruz, Elsa Carvalho,