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Abstract
Numerical computation is traditionally performed using floatingpoint arithmetic and truncated forms of infinite series, a methodology which allows for efficient computation at the cost of some accuracy. For most applications, these errors are entirely acceptable and the numerical results are considered trustworthy, but for some operations, we may want to have guarantees that the numerical results are correct, or explicit bounds on the errors. To obtain rigorous calculations, floatingpoint arithmetic is usually replaced by interval arithmetic and truncation errors are explicitly contained in the result. We may then ask the question of which mathematical operations can be implemented in a way in which the exact result can be approximated to arbitrary known accuracy by a numerical algorithm. This is the subject of computable analysis and forms a theoretical underpinning of rigorous numerical computation. The aim of this article is to provide a straightforward introduction to this subject that is powerful enough to answer questions arising in dynamic system theory.
Original language  English 

Article number  096012952000002 
Pages (fromto)  173233 
Number of pages  61 
Journal  Mathematical Structures in Computer Science 
Volume  30 
Issue number  2 
DOIs  
Publication status  Published  Feb 2020 
Keywords
 Computable analysis
 DIFFERENTIALINCLUSIONS
 REPRESENTATIONS
 THEORETIC APPROACH
 TOPOLOGICALSPACES
 Turing machine
 dynamic system
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 1 Talk or presentation  at conference

Verification of Hybrid Systems with Ariadne
Collins, P. (Speaker)
20 Nov 2020Activity: Talk or presentation / Performance / Speeches › Talk or presentation  at conference › Academic