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On the Solution of Large-scale Non-autonomous Differential Riccati Equations: a Numerical Study
Eugenio Mancinelli, Davide Palitta, Jens Saak
We explore the numerical solution of large-scale non-autonomous Differential Riccati Equations (DREs). While we assume to discretize the differential operator using a Backward Diff…
Generalizing Reduced Rank Extrapolation to Low-Rank Matrix Sequences
Pascal den Boef, Patrick Kürschner, Xiaobo Liu +5
Reduced rank extrapolation (RRE) is an acceleration method typically used to accelerate the iterative solution of nonlinear systems of equations using a fixed-point process. In thi…
Reduced rank extrapolation for multi-term Sylvester equations
Peter Benner, Pascal den Boef, Patrick Kürschner +2
We investigate the acceleration of stationary iterations for multi-term Sylvester equation by means of reduced rank extrapolation (RRE). Theoretical convergence results and impleme…
Towards a mixed-precision ADI method for Lyapunov equations
Jonas Schulze, Jens Saak
We apply mixed-precision to the low-rank Lyapunov ADI (LR-ADI) by performing certain aspects of the algorithm in a lower working precision. Namely, we accumulate the overall soluti…
Towards an Efficient Shifted Cholesky QR for Applications in Model Order Reduction using pyMOR
Maximilian Bindhak, Art J. R. Pelling, Jens Saak
Many model order reduction (MOR) methods rely on the computation of an orthonormal basis of a subspace onto which the large full order model is projected. Numerically, this entails…
A unifying framework for ADI-like methods for linear matrix equations and beneficial consequences
Jonas Schulze, Jens Saak
We derive the alternating-directions implicit (ADI) method based on a commuting operator split and apply the results in detail to the continuous time algebraic Lyapunov equation wi…