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Monte Carlo Complexity of Global Solution of Integral Equations

  • We study the problem of global solution of Fredholm integral equations. This means that we seek to approximate the full solution function (as opposed to the local problem, where only the value of the solution in a single point or a functional of the solution is sought). We analyze the Monte Carlo complexity, i.e. the complexity of stochastic solution of this problem. The framework for this analysis is provided by information based complexity theory. Our investigations complement previous ones on stochastic complexity of local solution and on deterministic complexity of both local and global solution. The results show that even in the global case Monte Carlo algorithms can perform better than deterministic ones, although the difference is not as large as in the local case.

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Author:Stefan Heinrich
URN (permanent link):urn:nbn:de:hbz:386-kluedo-49428
Serie (Series number):Interner Bericht des Fachbereich Informatik (289)
Document Type:Report
Language of publication:English
Publication Date:2017/10/25
Year of Publication:1997
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/10/25
Number of page:25
Faculties / Organisational entities:Fachbereich Informatik
DDC-Cassification:0 Allgemeines, Informatik, Informationswissenschaft / 004 Informatik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)