Convergence analysis for splitting of the abstract differential Riccati equation

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Sammanfattning

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.
Originalspråkengelska
Sidor (från-till)3128-3139
TidskriftSIAM Journal on Numerical Analysis
Volym52
Nummer6
DOI
StatusPublished - 2014

Bibliografisk information

The information about affiliations in this record was updated in December 2015.
The record was previously connected to the following departments: Numerical Analysis (011015004)

Ämnesklassifikation (UKÄ)

  • Matematik

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  • Tony Stillfjord

    Eskil Hansen (Första/primär/huvudhandledare)

    20112015

    Aktivitet: Examination och handledarskapHandledning av forskarstuderande

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