Guaranteed error bounds for linear algebra problems and a class of Picard-Lindelöf iteration methods

This study focuses on iteration methods based on the Banach fixed point theorem and a posteriori error estimates of Ostrowski. Their application for systems of linear simultaneous equations, bounded linear operators, as well as integral and differential equations is considered. The study presents a...

Täydet tiedot

Bibliografiset tiedot
Päätekijä: Matculevich, Svetlana
Muut tekijät: Informaatioteknologian tiedekunta, Faculty of Information Technology, Tietotekniikan laitos, Department of Mathematical Information Technology, University of Jyväskylä, Jyväskylän yliopisto
Aineistotyyppi: Pro gradu
Kieli:eng
Julkaistu: 2012
Aiheet:
Linkit: https://jyx.jyu.fi/handle/123456789/37373
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author Matculevich, Svetlana
author2 Informaatioteknologian tiedekunta Faculty of Information Technology Tietotekniikan laitos Department of Mathematical Information Technology University of Jyväskylä Jyväskylän yliopisto
author_facet Matculevich, Svetlana Informaatioteknologian tiedekunta Faculty of Information Technology Tietotekniikan laitos Department of Mathematical Information Technology University of Jyväskylä Jyväskylän yliopisto Matculevich, Svetlana Informaatioteknologian tiedekunta Faculty of Information Technology Tietotekniikan laitos Department of Mathematical Information Technology University of Jyväskylä Jyväskylän yliopisto
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description This study focuses on iteration methods based on the Banach fixed point theorem and a posteriori error estimates of Ostrowski. Their application for systems of linear simultaneous equations, bounded linear operators, as well as integral and differential equations is considered. The study presents a new version of the Picard–Lindelöf method for ordinary differential equations (ODEs) supplied with guaranteed and explicitly computable upper bounds of the approximation error. The estimates derived in the thesis take into account interpolation and integration errors and, therefore, provide objective information on the accuracy of computed approximations.
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spellingShingle Matculevich, Svetlana Guaranteed error bounds for linear algebra problems and a class of Picard-Lindelöf iteration methods Error estimates iterative method reliability the Picard–Lindelöf method guaranteed bounds Tietotekniikka Mathematical Information Technology 602 iterointi luotettavuus
title Guaranteed error bounds for linear algebra problems and a class of Picard-Lindelöf iteration methods
title_full Guaranteed error bounds for linear algebra problems and a class of Picard-Lindelöf iteration methods
title_fullStr Guaranteed error bounds for linear algebra problems and a class of Picard-Lindelöf iteration methods Guaranteed error bounds for linear algebra problems and a class of Picard-Lindelöf iteration methods
title_full_unstemmed Guaranteed error bounds for linear algebra problems and a class of Picard-Lindelöf iteration methods Guaranteed error bounds for linear algebra problems and a class of Picard-Lindelöf iteration methods
title_short Guaranteed error bounds for linear algebra problems and a class of Picard-Lindelöf iteration methods
title_sort guaranteed error bounds for linear algebra problems and a class of picard lindelöf iteration methods
title_txtP Guaranteed error bounds for linear algebra problems and a class of Picard-Lindelöf iteration methods
topic Error estimates iterative method reliability the Picard–Lindelöf method guaranteed bounds Tietotekniikka Mathematical Information Technology 602 iterointi luotettavuus
topic_facet 602 Error estimates Mathematical Information Technology Tietotekniikka guaranteed bounds iterative method iterointi luotettavuus reliability the Picard–Lindelöf method
url https://jyx.jyu.fi/handle/123456789/37373 http://www.urn.fi/URN:NBN:fi:jyu-201202151181
work_keys_str_mv AT matculevichsvetlana guaranteederrorboundsforlinearalgebraproblemsandaclassofpicardlindelöfiterat