Convergence analysis for splitting of the abstract differential Riccati equation
Hansen, Eskil LU and Stillfjord, Tony LU
(2014)
In SIAM Journal on Numerical Analysis
52(6).
p.3128-3139
- 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... (More) - 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4730126
- author
- Hansen, Eskil
LU
and Stillfjord, Tony
LU
- organization
- publishing date
- 2014
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Abstract differential Riccati equation, convergence order, splitting, low-rank approximation, Hilbert-Schmidt operators
- in
- SIAM Journal on Numerical Analysis
- volume
- 52
- issue
- 6
- pages
- 3128 - 3139
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- wos:000346842100023
- scopus:84919660473
- ISSN
- 0036-1429
- DOI
- 10.1137/130935501
- language
- English
- LU publication?
- yes
- additional info
- The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
- id
- 45005153-59d2-473f-af1a-7321b197a63f (old id 4730126)
- alternative location
- http://epubs.siam.org/doi/abs/10.1137/130935501
- date added to LUP
- 2016-04-01 10:17:20
- date last changed
- 2022-01-25 21:45:01
@article{45005153-59d2-473f-af1a-7321b197a63f,
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. <br/><br>
For a subsequent spatial discretization, the abstract setting also yields uniform temporal error bounds with respect to the spatial discretization parameter. <br/><br>
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.}},
author = {{Hansen, Eskil and Stillfjord, Tony}},
issn = {{0036-1429}},
keywords = {{Abstract differential Riccati equation; convergence order; splitting; low-rank approximation; Hilbert-Schmidt operators}},
language = {{eng}},
number = {{6}},
pages = {{3128--3139}},
publisher = {{Society for Industrial and Applied Mathematics}},
series = {{SIAM Journal on Numerical Analysis}},
title = {{Convergence analysis for splitting of the abstract differential Riccati equation}},
url = {{https://lup.lub.lu.se/search/files/1713918/4730128.pdf}},
doi = {{10.1137/130935501}},
volume = {{52}},
year = {{2014}},
}