Convergence analysis for splitting of the abstract differential Riccati equation

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

Abstract

We consider a splitting-based approximation of the abstract differential Riccati equation in the setting of Hilbert--Schmidt operators. The Riccati equation arises in many different areas and is important within the field of optimal control. In this paper we conduct a temporal error analysis and prove that the splitting method converges with the same order as the implicit Euler scheme, under the same low regularity requirements on the initial values.
For a subsequent spatial discretization, the abstract setting also yields uniform temporal error bounds with respect to the spatial discretization parameter.
The spatial discretizations commonly lead to large-scale problems, where the use of structural properties of the solution is essential. We therefore conclude by proving that the splitting method preserves low-rank structure in the matrix-valued case. Numerical results demonstrate the validity of the convergence analysis.

Detaljer

Författare
Enheter & grupper
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematik

Nyckelord

Originalspråkengelska
Sidor (från-till)3128-3139
TidskriftSIAM Journal on Numerical Analysis
Volym52
Utgåva nummer6
StatusPublished - 2014
PublikationskategoriForskning
Peer review utfördJa

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Relaterad forskningsoutput

Tony Stillfjord, 2015, Centre for Mathematical Sciences, Lund University. 129 s.

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