ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0 Online Edition Research Article
Antti Koskela,
Hermann Mena
S. 431 - 454 doi:10.1553/etna_vol52s431 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol52s431
Abstract: We consider a Krylov subspace approximation method for the symmetric differential Riccati equation$\dot{X} = AX + XA^T + Q - XSX$, $X(0)=X_0$. The method we consider is based on projectingthe large-scale equation onto a Krylov subspace spanned by the matrix $A$ and the low-rank factors of $X_0$ and $Q$.We prove that the method is structure preserving in the sense that it preservestwo important properties of the exact flow, namely the positivity of the exact flowand also the property of monotonicity. We provide a theoretical a priori error analysis thatshows superlinear convergence of the method.Moreover, we derive an a posteriori error estimate that is shown to be effective in numerical examples. Keywords: differential Riccati equations, LQR optimal control problems, large-scale ordinary differential equations, Krylov subspace methods, matrix exponential, exponential integrators, model order reduction, low-rank approximation Published Online: 2020/09/17 11:48:43 Object Identifier: 0xc1aa5576 0x003bd61b Rights: . Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613. …
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |