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Numerical Algorithms

, Volume 78, Issue 4, pp 1129–1151 | Cite as

Adaptive high-order splitting schemes for large-scale differential Riccati equations

  • Tony Stillfjord
Open Access
Original Paper

Abstract

We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical to employ structural properties of the matrix-valued solution, or the computational cost and storage requirements become infeasible. Our main contribution is therefore to formulate these high-order splitting schemes in an efficient way by utilizing a low-rank factorization. Previous results indicated that this was impossible for methods of order higher than 2, but our new approach overcomes these difficulties. In addition, we demonstrate that the proposed methods contain natural embedded error estimates. These may be used, e.g., for time step adaptivity, and our numerical experiments in this direction show promising results.

Keywords

Differential Riccati equations Large-scale Splitting schemes High order Adaptivity 

Mathematics Subject Classification (2010)

15A24 49N10 65L05 93A15 

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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Mathematical SciencesChalmers University of Technology and the University of GothenburgGöteborgSweden

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