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Adaptive high-order splitting schemes for large-scale differential Riccati equations. (English) Zbl 1404.65060

Author’s 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.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
15A24 Matrix equations and identities
65F30 Other matrix algorithms (MSC2010)
93A15 Large-scale systems

Software:

MESS
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References:

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