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Autor:
Bertram, Christian, Faßbender, Heike
A class of (block) rational Krylov subspace based projection method for solving large-scale continuous-time algebraic Riccati equation (CARE) $0 = \mathcal{R}(X) := A^HX + XA + C^HC - XBB^HX$ with a large, sparse $A$ and $B$ and $C$ of full low rank
Externí odkaz:
http://arxiv.org/abs/2312.08855
Autor:
Bertram, Christian, Faßbender, Heike
In [3] it was shown that four seemingly different algorithms for computing low-rank approximate solutions $X_j$ to the solution $X$ of large-scale continuous-time algebraic Riccati equations (CAREs) $0 = \mathcal{R}(X) := A^HX+XA+C^HC-XBB^HX $ genera
Externí odkaz:
http://arxiv.org/abs/2304.01624
Autor:
Bertram, Christian, Faßbender, Heike
Publikováno v:
In Linear Algebra and Its Applications 15 April 2024 687:38-67
Autor:
Løkkegaard, Martin1 (AUTHOR) mloek@mek.dtu.dk, Bertram, Christian Alexander1 (AUTHOR), Mortensen, Niels Henrik1 (AUTHOR), Hvam, Lars2 (AUTHOR), Haug, Anders3 (AUTHOR)
Publikováno v:
International Journal of Production Research. Feb2023, Vol. 61 Issue 4, p1358-1372. 15p. 1 Diagram, 2 Charts, 4 Graphs.
Autor:
Bertram, Christian, Faßbender, Heike
The approximate solution of large-scale algebraic Riccati equations is considered. We are interested in approximate solutions which yield a Riccati residual matrix of a particular small rank. It is assumed that such approximate solutions can be writt
Externí odkaz:
http://arxiv.org/abs/2004.11212
Autor:
Bertram, Christian, Faßbender, Heike
We analyze a family of Runge-Kutta based quadrature algorithms for the approximation of the gramians of linear time invariant dynamical systems. The approximated gramians are used to obtain an approximate balancing transformation similar to the appro
Externí odkaz:
http://arxiv.org/abs/2003.03101
Akademický článek
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Autor:
Bertram, Christian, Faßbender, Heike
This paper introduces a novel framework for the solution of (large-scale) Lyapunov and Sylvester equations derived from numerical integration methods. Suitable systems of ordinary differential equations are introduced. Low-rank approximations of thei
Externí odkaz:
http://arxiv.org/abs/1903.05383
Autor:
Bertram, Christian, Faßbender, Heike
Publikováno v:
In Linear Algebra and Its Applications 1 August 2021 622:66-103