6 citations · 12 across the 6 of their papers we have counts for
6 papers
Implicit Peer Triplets in Gradient-Based Solution Algorithms for ODE Constrained Optimal Control
Jens Lang, Bernhard A. Schmitt
It is common practice to apply gradient-based optimization algorithms to numerically solve large-scale ODE constrained optimal control problems. Gradients of the objective function…
A Stiff MOL Boundary Control Problem for the 1D Heat Equation with Exact Discrete Solution
Jens Lang, Bernhard A. Schmitt
Method-of-lines discretizations are demanding test problems for stiff integration methods. However, for PDE problems with known analytic solution the presence of space discretizati…
Krylov Methods for Adjoint-Free Singular Vector Based Perturbations in Dynamical Systems
Jens Winkler, Michael Denhard, Bernhard A. Schmitt
The estimation of weather forecast uncertainty with ensemble systems requires a careful selection of perturbations to establish a reliable sampling of the error growth potential in…
Implicit A-Stable Peer Triplets for ODE Constrained Optimal Control Problems
Jens Lang, Bernhard A. Schmitt
This paper is concerned with the construction and convergence analysis of novel implicit Peer triplets of two-step nature with four stages for nonlinear ODE constrained optimal con…
Discrete Adjoint Implicit Peer Methods in Optimal Control
Jens Lang, Bernhard A. Schmitt
It is well known that in the first-discretize-then-optimize approach in the control of ordinary differential equations the adjoint method may converge under additional order condit…
Algebraic criteria for A-stability of peer two-step methods
Bernhard A. Schmitt
A new criterion for A-stability of peer two-step methods is presented which is verifiable exactly in exact arithmetic by checking semi-definiteness of a certain test matrix. It dep…