3 citations · 6 across the 5 of their papers we have counts for
6 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…
Higher-order derivatives of the QR and of the real symmetric eigenvalue decomposition in forward and reverse mode algorithmic differentiation
Sebastian F. Walter, Lutz Lehmann, René Lamour
We address the task of higher-order derivative evaluation of computer programs that contain QR decompositions and real symmetric eigenvalue decompositions. The approach is a combin…
Algorithmic Differentiation of Linear Algebra Functions with Application in Optimum Experimental Design (Extended Version)
S. F. Walter, L. Lehmann
We derive algorithms for higher order derivative computation of the rectangular and eigenvalue decomposition of symmetric matrices with distinct eigenvalues in the forward and…