GPU acceleration of splitting schemes applied to differential matrix equations
Mena, Hermann ; Pfurtscheller, Lena Maria and Stillfjord, Tony LU
(2019)
In Numerical Algorithms
83(1).
p.395-419
- Abstract
We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their solution, one may use several different kinds of numerical methods. Of these, splitting schemes are often a very competitive choice. In this article, we investigate the use of graphical processing units (GPUs) to parallelize such schemes and thereby further increase their effectiveness. According to our numerical experiments, large speed-ups are often observed for sufficiently large matrices. We also provide a comparison between different splitting strategies, demonstrating that splitting the equations into a... (More)
We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their solution, one may use several different kinds of numerical methods. Of these, splitting schemes are often a very competitive choice. In this article, we investigate the use of graphical processing units (GPUs) to parallelize such schemes and thereby further increase their effectiveness. According to our numerical experiments, large speed-ups are often observed for sufficiently large matrices. We also provide a comparison between different splitting strategies, demonstrating that splitting the equations into a moderate number of subproblems is generally optimal.
(Less)
- author
- Mena, Hermann
; Pfurtscheller, Lena Maria
and Stillfjord, Tony
LU
- publishing date
- 2019-04-05
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Differential Lyapunov equations, Differential Riccati equations, GPU acceleration, Large scale, Splitting schemes
- in
- Numerical Algorithms
- volume
- 83
- issue
- 1
- pages
- 25 pages
- publisher
- Springer
- external identifiers
-
- scopus:85064342095
- ISSN
- 1017-1398
- DOI
- 10.1007/s11075-019-00687-w
- language
- English
- LU publication?
- no
- additional info
- Funding Information: Open access funding provided by Max Planck Society. The authors would like to thank the anonymous referees, whose critical and constructive comments greatly improved the manuscript. We are also grateful to Peter Kandolf for his assistance with the original expleja code. Publisher Copyright: © 2019, The Author(s).
- id
- 1218f238-f3a5-45ab-9170-bf56c757d7b8
- date added to LUP
- 2024-01-23 17:40:44
- date last changed
- 2024-02-26 09:07:59
@article{1218f238-f3a5-45ab-9170-bf56c757d7b8,
abstract = {{<p>We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their solution, one may use several different kinds of numerical methods. Of these, splitting schemes are often a very competitive choice. In this article, we investigate the use of graphical processing units (GPUs) to parallelize such schemes and thereby further increase their effectiveness. According to our numerical experiments, large speed-ups are often observed for sufficiently large matrices. We also provide a comparison between different splitting strategies, demonstrating that splitting the equations into a moderate number of subproblems is generally optimal.</p>}},
author = {{Mena, Hermann and Pfurtscheller, Lena Maria and Stillfjord, Tony}},
issn = {{1017-1398}},
keywords = {{Differential Lyapunov equations; Differential Riccati equations; GPU acceleration; Large scale; Splitting schemes}},
language = {{eng}},
month = {{04}},
number = {{1}},
pages = {{395--419}},
publisher = {{Springer}},
series = {{Numerical Algorithms}},
title = {{GPU acceleration of splitting schemes applied to differential matrix equations}},
url = {{http://dx.doi.org/10.1007/s11075-019-00687-w}},
doi = {{10.1007/s11075-019-00687-w}},
volume = {{83}},
year = {{2019}},
}