Computable analysis with applications to dynamic systems

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Numerical computation is traditionally performed using floating-point 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, floating-point 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 languageEnglish
Article number096012952000002
Pages (from-to)173-233
Number of pages61
JournalMathematical Structures in Computer Science
Volume30
Issue number2
DOIs
Publication statusPublished - Feb 2020

Keywords

  • Computable analysis
  • DIFFERENTIAL-INCLUSIONS
  • REPRESENTATIONS
  • THEORETIC APPROACH
  • TOPOLOGICAL-SPACES
  • Turing machine
  • dynamic system

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