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

Authors :
Stillfjord, Tony
Source :
Numerical Algorithms; Aug2018, Vol. 78 Issue 4, p1129-1151, 23p
Publication Year :
2018

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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10171398
Volume :
78
Issue :
4
Database :
Complementary Index
Journal :
Numerical Algorithms
Publication Type :
Academic Journal
Accession number :
130722887
Full Text :
https://doi.org/10.1007/s11075-017-0416-8