Time complexity and convergence analysis of domain theoretic Picard method

Amin Farjudian, Michal Konečný

Research output: Chapter in Book/Conference proceedingConference contributionpeer-review

5 Citations (Scopus)

Abstract

We present an implementation of the domain-theoretic Picard method for solving initial value problems (IVPs) introduced by Edalat and Pattinson [1]. Compared to Edalat and Pattinson's implementation, our algorithm uses a more efficient arithmetic based on an arbitrary precision floating-point library. Despite the additional overestimations due to floating-point rounding, we obtain a similar bound on the convergence rate of the produced approximations. Moreover, our convergence analysis is detailed enough to allow a static optimisation in the growth of the precision used in successive Picard iterations. Such optimisation greatly improves the efficiency of the solving process. Although a similar optimisation could be performed dynamically without our analysis, a static one gives us a significant advantage: we are able to predict the time it will take the solver to obtain an approximation of a certain (arbitrarily high) quality.

Original languageEnglish
Title of host publicationLogic, Language, Information and Computation - 15th International Workshop, WoLLIC 2008, Proceedings
Pages149-163
Number of pages15
DOIs
Publication statusPublished - 2008
Externally publishedYes
Event15th International Workshop on Logic, Language, Information and Computation, WoLLIC 2008 - Edinburgh, United Kingdom
Duration: 1 Jul 20084 Jul 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5110 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference15th International Workshop on Logic, Language, Information and Computation, WoLLIC 2008
Country/TerritoryUnited Kingdom
CityEdinburgh
Period1/07/084/07/08

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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