4 papers
An Open Newton Method for Piecewise Smooth Functions
Manuel Radons, Lutz Lehmann, Tom Streubel +1
Recent research has shown that piecewise smooth (PS) functions can be approximated by piecewise linear functions with second order error in the distance to a given reference point.…
Sign controlled solvers for the absolute value equation with an application to support vector machines
Lutz Lehmann, Manuel Radons, Siegfried M. Rump +1
Let be a real matrix and . The piecewise linear equation system is called an absolute value equation. It is equivalent to…
Integrating Lipschitzian Dynamical Systems using Piecewise Algorithmic Differentiation
Andreas Griewank, Richard Hasenfelder, Manuel Radons +1
In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side \(F:\R^n\to\R^n\). When applied to such a problem the cla…
Piecewise linear secant approximation via Algorithmic Piecewise Differentiation
Andreas Griewank, Tom Streubel, Lutz Lehmann +2
It is shown how piecewise differentiable functions that are defined by evaluation programs can be approximated locally by a piecewise linear m…