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Wrapping in exact real arithmetic
Post-edited
Authors : Müller, Norbert (Author of the conference)
CIRM (Publisher )
03D60 - Computability and recursion theory on ordinals, admissible sets, etc.
65Y15 - Packaged methods in numerical analysis
68Q25 - Analysis of algorithms and problem complexity
CIRM (Publisher )
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| computability on real numbers exact real arithmetic wrapping effects Taylor models example 1 : logistic map example 2 : Van der Pol oscillator |
Abstract :
A serious problem common to all interval algorithms is that they suffer from wrapping effects, i.e. unnecessary growth of approximations during a computation. This is essentially connected to functional dependencies inside vectors of data computed from the same inputs. Reducing these effects is an important issue in interval arithmetic, where the most successful approach uses Taylor models.
In TTE Taylor models have not been considered explicitly, as they use would not change the induced computability, already established using ordinary interval computations. However for the viewpoint of efficiency, they lead to significant improvements.
In the talk we report on recent improvements on the iRRAM software for exact real arithmetic (ERA) based on Taylor models. The techniques discussed should also easily be applicable to other software for exact real computations as long as they also are based on interval arithmetic.
As instructive examples we consider the one-dimensional logistic map and a few further discrete dynamical systems of higher dimensions
Joint work with Franz Brauße, Trier, and Margarita Korovina, Novosibirsk.
MSC Codes : In TTE Taylor models have not been considered explicitly, as they use would not change the induced computability, already established using ordinary interval computations. However for the viewpoint of efficiency, they lead to significant improvements.
In the talk we report on recent improvements on the iRRAM software for exact real arithmetic (ERA) based on Taylor models. The techniques discussed should also easily be applicable to other software for exact real computations as long as they also are based on interval arithmetic.
As instructive examples we consider the one-dimensional logistic map and a few further discrete dynamical systems of higher dimensions
Joint work with Franz Brauße, Trier, and Margarita Korovina, Novosibirsk.
03D60 - Computability and recursion theory on ordinals, admissible sets, etc.
65Y15 - Packaged methods in numerical analysis
68Q25 - Analysis of algorithms and problem complexity
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 03/02/16 Conference Date : 12/01/16 Subseries : Research talks arXiv category : Logic ; Computer Science Mathematical Area(s) : Computer Science ; Logic and Foundations Format : MP4 (.mp4) - HD Video Time : 00:59:51 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-01-12_Muller.mp4 
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Information on the Event
Event Title : Effective analysis: foundations, implementations, certification / Analyse effective: fondations, programmation, certificationEvent Organizers : Mahboubi, Assia ; Schuster, Peter ; Spitters, Bas Dates : 11/01/16 - 15/01/16 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1508.html
Citation Data
DOI : 10.24350/CIRM.V.18914503Cite this video as: Müller, Norbert (2016). Wrapping in exact real arithmetic. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18914503 URI : http://dx.doi.org/10.24350/CIRM.V.18914503 |
See Also
- [Multi angle] Verified numerics for ODEs in Isabelle/HOL / Author of the conference Immler, Fabian.
- [Multi angle] Programming with numerical uncertainties / Author of the conference Darulova, Eva.
- [Multi angle] Formal verification of numerical analysis programs / Author of the conference Boldo, Sylvie.
- [Multi angle] Proof and computation in Coq / Author of the conference Théry, Laurent.
Bibliography
- iRRAM homepage - http://irram.uni-trier.de/
- GitHub - Norbert Müller/iRRAM: Exact real arithmetic in C++ - https://github.com/norbert-mueller/iRRAM
