Computing the Bouligand derivative of a class of piecewise-differentiable flows

2016/12/08 by Shai Revzen, Revzen, Shai, Samuel A Burden +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1612.02763

arxiv created 2016/12/08 · arxiv updated 2016/12/09

Abstract

Event--selected C^r 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 (d!) in the dimension (d) of the space, precluding a polynomial-time algorithm. We show how an exponential number (2^d) 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 d of these points.

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