41 citations · 58 across the 5 of their papers we have counts for
7 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.…
High dimensional integration of kinks and jumps -- smoothing by preintegration
Andreas Griewank, Frances Y. Kuo, Hernan Leövey +1
We show how simple kinks and jumps of otherwise smooth integrands over can be dealt with by a preliminary integration with respect to a single well chosen variable.…
Solving piecewise linear equations in abs-normal form
Andreas Griewank, Jens Uwe Bernt, Manuel Radons +1
With the ultimate goal of iteratively solving piecewise smooth (PS) systems, we consider the solution of piecewise linear (PL) equations. PL models can be derived in the fashion of…
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…
Applicability of Quasi-Monte Carlo for lattice systems
Andreas Ammon, Tobias Hartung, Karl Jansen +3
This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theor…
Quasi-Monte Carlo methods for lattice systems: a first look
K. Jansen, H. Leovey, A. Ammon +2
We investigate the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables fo…