Multipoint methods for solving nonlinear equations: a survey

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dc.contributor.authorPetkovic, Miodrag S.
dc.contributor.authorNeta, Beny
dc.contributor.authorPetkovic, Ljiljana D.
dc.contributor.authorDzunic, Jovana
dc.contributor.departmentApplied Mathematicsen_US
dc.date.accessioned2014-03-12T22:47:48Z
dc.date.available2014-03-12T22:47:48Z
dc.date.issued2014
dc.descriptionApplied Mathematics and Computation, 226, (2014), 635–640.en_US
dc.descriptionThe article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2013.10.072en_US
dc.description.abstractMultipoint iterative methods belong to the class of the most efficient methods for solving nonlinear equations. Recent interest in the research and development of this type of meth- ods has arisen from their capability to overcome theoretical limits of one-point methods concerning the convergence order and computational efficiency. This survey paper is a mixture of theoretical results and algorithmic aspects and it is intended as a review of the most efficient root-finding algorithms and developing techniques in a general sense. Many existing methods of great efficiency appear as special cases of presented general iter- ative schemes. Special attention is devoted to multipoint methods with memory that use already computed information to considerably increase convergence rate without addi- tional computational costs. Some classical results of the 1970s which have had a great influence to the topic, often neglected or unknown to many readers, are also included not only as historical notes but also as genuine sources of many recent ideas. To a certain degree, the presented study follows in parallel main themes shown in the recently pub- lished book (Petkovic ́ et al., 2013) [53], written by the authors of this paper.en_US
dc.identifier.urihttps://hdl.handle.net/10945/39425
dc.publisherElsevier
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.subject.authorNonlinear equationsen_US
dc.subject.authorIterative methodsen_US
dc.subject.authorMultipoint methodsen_US
dc.subject.authorComputational efficiencyen_US
dc.subject.authorConvergence rateen_US
dc.subject.authorAcceleration of convergenceen_US
dc.titleMultipoint methods for solving nonlinear equations: a surveyen_US
dc.typeArticle
dspace.entity.typePublication
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