Multipoint methods for solving nonlinear equations: a survey

Download
Author
Petkovic, Miodrag S.
Neta, Beny
Petkovic, Ljiljana D.
Dzunic, Jovana
Date
2014Metadata
Show full item recordAbstract
Multipoint 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.
Description
Applied Mathematics and Computation, 226, (2014), 635–640.
The article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2013.10.072
Rights
This 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.Collections
Related items
Showing items related by title, author, creator and subject.
-
Modeling and Simulation Tool to Enhance and Explore the ROE Design Space for NLW
Hall, Steven B. (Monterey, California: Naval Postgraduate SchoolMonterey, California. Naval Postgraduate School, 2019-12); NPS-19-M238-AThe goal of this research is to define an analytical tool, Workbench for refining Rules of Engagement against Crowd Hostiles (WRENCH), that will support operational planners and ground commanders in defining contextually ... -
Modeling and Simulation Tool to Enhance and Explore the ROE Design Space for NLW
Hall, Steven B. (Monterey, California: Naval Postgraduate SchoolMonterey, California. Naval Postgraduate School, 2019-12); NPS-19-M238-AThe goal of this research is to define an analytical tool, Workbench for refining Rules of Engagement against Crowd Hostiles (WRENCH), that will support operational planners and ground commanders in defining contextually ... -
Counter Directed Energy Warfare (CDEW)
Blau, Joseph A.; Johnson, Bonnie W.; Cohn, Keith; Green, John (Monterey, California: Naval Postgraduate SchoolMonterey, California. Naval Postgraduate School, 2019-12); NPS-19-N003-ADirected Energy Weapons (DEW) will proliferate and become a threat exploited by adversaries due to high potential mission success and low cost compared to traditional weapons. Counter DEW (CDEW) methods and capabilities ...