Computing the Bouligand derivative of a class of piecewise-differentiable flows
Dynamical Systems
2016-12-09 v1
Abstract
Event--selected vector fields yield piecewise-differentiable flows, which possess a continuous and piecewise-linear Bouligand (or B-)derivative; here we provide an algorithm for computing this B-derivative. The number of "pieces" of the piecewise-linear B-derivative is factorial () in the dimension () of the space, precluding a polynomial-time algorithm. We show how an exponential number () of points can be used to represent the B-derivative as a piecewise-linear homeomorphism in such a way that evaluating the derivative reduces to linear algebra computations involving a matrix constructed from of these points.
Keywords
Cite
@article{arxiv.1612.02763,
title = {Computing the Bouligand derivative of a class of piecewise-differentiable flows},
author = {Shai Revzen and Samuel A Burden},
journal= {arXiv preprint arXiv:1612.02763},
year = {2016}
}