Zobrazeno 1 - 10
of 207
pro vyhledávání: '"Saak, Jens"'
Autor:
Schulze, Jonas, Saak, Jens
We derive the Alternating-Direction Implicit (ADI) method based on a commuting operator split and apply the results to the continuous time algebraic Lyapunov equation with low-rank constant term and approximate solution. Previously, it has been manda
Externí odkaz:
http://arxiv.org/abs/2406.13477
Autor:
Saak, Jens, Werner, Steffen W. R.
Publikováno v:
Electron. Trans. Numer. Anal., 62:95-118, 2024
Continuous-time algebraic Riccati equations can be found in many disciplines in different forms. In the case of small-scale dense coefficient matrices, stabilizing solutions can be computed to all possible formulations of the Riccati equation. This i
Externí odkaz:
http://arxiv.org/abs/2402.06844
Sequences of parametrized Lyapunov equations can be encountered in many application settings. Moreover, solutions of such equations are often intermediate steps of an overall procedure whose main goal is the computation of $\text{trace}(EX)$ where $X
Externí odkaz:
http://arxiv.org/abs/2312.08201
Autor:
Saak, Jens, Schulze, Jonas
We suggest a technique to reduce the storage size of sparse matrices at no loss of information. We call this technique Diagonally-Adressed (DA) storage. It exploits the typically low matrix bandwidth of matrices arising in applications. For memory-bo
Externí odkaz:
http://arxiv.org/abs/2307.06305
The race for the most efficient, accurate, and universal algorithm in scientific computing drives innovation. At the same time, this healthy competition is only beneficial if the research output is actually comparable to prior results. Fairly compari
Externí odkaz:
http://arxiv.org/abs/2307.00137
Autor:
Boege, Tobias, Fritze, René, Görgen, Christiane, Hanselman, Jeroen, Iglezakis, Dorothea, Kastner, Lars, Koprucki, Thomas, Krause, Tabea, Lehrenfeld, Christoph, Polla, Silvia, Reidelbach, Marco, Riedel, Christian, Saak, Jens, Schembera, Björn, Tabelow, Karsten, Weber, Marcus
In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of research-data management and planning. A number of decentralized approaches are presented and compared to needs and challenges faced in
Externí odkaz:
http://arxiv.org/abs/2211.12071
We discuss the feedback control problem for a two-dimensional two-phase Stefan problem. In our approach, we use a sharp interface representation in combination with mesh-movement to track the interface position. To attain a feedback control, we apply
Externí odkaz:
http://arxiv.org/abs/2209.05476
Computational methods for reducing the complexity of Finite Element (FE) models in structural dynamics are usually based on modal analysis. Classical approaches such as modal truncation, static condensation (Craig-Bampton, Guyan), and component mode
One of the most computationally expensive steps of the low-rank ADI method for large-scale Lyapunov equations is the solution of a shifted linear system at each iteration. We propose the use of the extended Krylov subspace method for this task. In pa
Externí odkaz:
http://arxiv.org/abs/2203.17174
In this paper, we generalize existing frameworks for $\mathcal{H}_2\otimes\mathcal{L}_2$-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary ptimality conditions for
Externí odkaz:
http://arxiv.org/abs/2103.03136