On Some Multipoint Methods Arrising from Optimal in the Sense of Kung-Traub Algorithms for Numerical Solution of Nonlinear Equations

On Some Multipoint Methods Arrising from Optimal in the Sense of Kung-Traub Algorithms for Numerical Solution of Nonlinear Equations

In this paper we will examine self-accelerating in terms of convergence speed and the corresponding index of eciency in the sense of Ostrowski - Traub of certain standard and most commonly used in practice multipoint iterative methods using several initial approximations for numerical solution of no...

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Main Authors: Nikolay Kyurkchiev, Anton Iliev
Format: Article
Language:English
Published: Biomath Forum 2013-07-01
Series:Biomath
Online Access:http://www.biomathforum.org/biomath/index.php/biomath/article/view/168
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spelling doaj-597ba5f1bdfb41bca599689d13f5e6e92020-11-25T01:13:33ZengBiomath ForumBiomath1314-684X1314-72182013-07-012110.11145/168135On Some Multipoint Methods Arrising from Optimal in the Sense of Kung-Traub Algorithms for Numerical Solution of Nonlinear EquationsNikolay Kyurkchiev0Anton Iliev1Faculty of Mathematics and Informatics Paisii Hilendarski University of Plovdiv 236, Bulgaria Blvd., 4003 Plovdiv, BulgariaFaculty of Mathematics and Informatics Paisii Hilendarski University of Plovdiv 236, Bulgaria Blvd., 4003 PlovdivIn this paper we will examine self-accelerating in terms of convergence speed and the corresponding index of eciency in the sense of Ostrowski - Traub of certain standard and most commonly used in practice multipoint iterative methods using several initial approximations for numerical solution of nonlinear equations due to optimal in the sense of the Kung-Traub algorithm of order 4, 8 and 16. Some hypothetical iterative procedures generated by algorithms from order of convergence 32 and 64 are also studied (the receipt and publication of which is a matter of time, having in mind the increased interest in such optimal algorithms). The corresponding model theorems for their convergence speed and eciency index have been formulated and proved.http://www.biomathforum.org/biomath/index.php/biomath/article/view/168
collection DOAJ
language English
format Article
sources DOAJ
author Nikolay Kyurkchiev
Anton Iliev
spellingShingle Nikolay Kyurkchiev
Anton Iliev
On Some Multipoint Methods Arrising from Optimal in the Sense of Kung-Traub Algorithms for Numerical Solution of Nonlinear Equations
Biomath
author_facet Nikolay Kyurkchiev
Anton Iliev
author_sort Nikolay Kyurkchiev
title On Some Multipoint Methods Arrising from Optimal in the Sense of Kung-Traub Algorithms for Numerical Solution of Nonlinear Equations
title_short On Some Multipoint Methods Arrising from Optimal in the Sense of Kung-Traub Algorithms for Numerical Solution of Nonlinear Equations
title_full On Some Multipoint Methods Arrising from Optimal in the Sense of Kung-Traub Algorithms for Numerical Solution of Nonlinear Equations
title_fullStr On Some Multipoint Methods Arrising from Optimal in the Sense of Kung-Traub Algorithms for Numerical Solution of Nonlinear Equations
title_full_unstemmed On Some Multipoint Methods Arrising from Optimal in the Sense of Kung-Traub Algorithms for Numerical Solution of Nonlinear Equations
title_sort on some multipoint methods arrising from optimal in the sense of kung-traub algorithms for numerical solution of nonlinear equations
publisher Biomath Forum
series Biomath
issn 1314-684X
1314-7218
publishDate 2013-07-01
description In this paper we will examine self-accelerating in terms of convergence speed and the corresponding index of eciency in the sense of Ostrowski - Traub of certain standard and most commonly used in practice multipoint iterative methods using several initial approximations for numerical solution of nonlinear equations due to optimal in the sense of the Kung-Traub algorithm of order 4, 8 and 16. Some hypothetical iterative procedures generated by algorithms from order of convergence 32 and 64 are also studied (the receipt and publication of which is a matter of time, having in mind the increased interest in such optimal algorithms). The corresponding model theorems for their convergence speed and eciency index have been formulated and proved.
url http://www.biomathforum.org/biomath/index.php/biomath/article/view/168
work_keys_str_mv AT nikolaykyurkchiev onsomemultipointmethodsarrisingfromoptimalinthesenseofkungtraubalgorithmsfornumericalsolutionofnonlinearequations
AT antoniliev onsomemultipointmethodsarrisingfromoptimalinthesenseofkungtraubalgorithmsfornumericalsolutionofnonlinearequations
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