An efficient method for the numerical evaluation of partial derivatives of arbitrary order
ACM Transactions on Mathematical Software (TOMS)
Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
ACM Transactions on Mathematical Software (TOMS)
Evaluating higher derivative tensors by forward propagation of univariate Taylor series
Mathematics of Computation
Local Versus Global Strategies for Adaptive Quadrature
ACM Transactions on Mathematical Software (TOMS)
New Quadrature Formulas from Conformal Maps
SIAM Journal on Numerical Analysis
Bivariate Product Cubature Using Peano Kernels for Local Error Estimates
Journal of Scientific Computing
On the implementation of automatic differentiation tools
Higher-Order and Symbolic Computation
Fast higher-order derivative tensors with Rapsodia
Optimization Methods & Software
Introduction to Interval Analysis
Introduction to Interval Analysis
On Generalized Gaussian Quadrature Rules for Singular and Nearly Singular Integrals
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
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.