Efficient Three-Step Class of Eighth-Order Multiple Root Solvers and Their Dynamics

This article proposes a wide general class of optimal eighth-order techniques for approximating multiple zeros of scalar nonlinear equations. The new strategy adopts a weight function with an approach involving the function-to-function ratio. An extensive convergence analysis is performed for the ei...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry (Basel) 2019-07, Vol.11 (7), p.837
Main Authors: Alharbey, R. A., Kansal, Munish, Behl, Ramandeep, Machado, J. A. Tenreiro
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Global positioning systems
GPS
multiple roots
Neighborhoods
Nonlinear equations
optimal iterative methods
order of convergence
scalar equations
Weighting functions
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c364t-97f3403d8fedabe86017ba6a7aaec56484fbdadce22addb5d2164e98f5e270a43
cites cdi_FETCH-LOGICAL-c364t-97f3403d8fedabe86017ba6a7aaec56484fbdadce22addb5d2164e98f5e270a43
container_end_page
container_issue 7
container_start_page 837
container_title Symmetry (Basel)
container_volume 11
creator Alharbey, R. A.
Kansal, Munish
Behl, Ramandeep
Machado, J. A. Tenreiro
description This article proposes a wide general class of optimal eighth-order techniques for approximating multiple zeros of scalar nonlinear equations. The new strategy adopts a weight function with an approach involving the function-to-function ratio. An extensive convergence analysis is performed for the eighth-order convergence of the algorithm. It is verified that some of the existing techniques are special cases of the new scheme. The algorithms are tested in several real-life problems to check their accuracy and applicability. The results of the dynamical study confirm that the new methods are more stable and accurate than the existing schemes.
doi_str_mv 10.3390/sym11070837
format article
fullrecord <record><control><sourceid>proquest_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_2cebf2ae2fa346288d4dea7300b1835a</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><doaj_id>oai_doaj_org_article_2cebf2ae2fa346288d4dea7300b1835a</doaj_id><sourcerecordid>2550259205</sourcerecordid><originalsourceid>FETCH-LOGICAL-c364t-97f3403d8fedabe86017ba6a7aaec56484fbdadce22addb5d2164e98f5e270a43</originalsourceid><addsrcrecordid>eNpNkU9Lw0AQxYMoWLQnv8CCR4lu9k-yOUqtWqgUbD0vk-xsuyXNxt1U6Lc3WpHOZYbhze8NvCS5yeg95yV9iIddltGCKl6cJSNGC56qshTnJ_NlMo5xS4eSVIqcjpLl1FpXO2x7stoExHTZY0cmDcRIvCVTt970m3QRDAbytm961zVI3r3vydI3XxgigdYMp-gCeTq0sHN1vE4uLDQRx3_9Kvl4nq4mr-l88TKbPM7TmueiT8vCckG5URYNVKhymhUV5FAAYC1zoYStDJgaGQNjKmlYlgsslZXICgqCXyWzI9d42OouuB2Eg_bg9O_Ch7WG0Lu6Qc1qrCwDZBa4yJlSRhiEglNaZYpLGFi3R1YX_OceY6-3fh_a4X3NpKRMlozKQXV3VNXBxxjQ_rtmVP-EoE9C4N84knnx</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2550259205</pqid></control><display><type>article</type><title>Efficient Three-Step Class of Eighth-Order Multiple Root Solvers and Their Dynamics</title><source>Access via ProQuest (Open Access)</source><creator>Alharbey, R. A. ; Kansal, Munish ; Behl, Ramandeep ; Machado, J. A. Tenreiro</creator><creatorcontrib>Alharbey, R. A. ; Kansal, Munish ; Behl, Ramandeep ; Machado, J. A. Tenreiro</creatorcontrib><description>This article proposes a wide general class of optimal eighth-order techniques for approximating multiple zeros of scalar nonlinear equations. The new strategy adopts a weight function with an approach involving the function-to-function ratio. An extensive convergence analysis is performed for the eighth-order convergence of the algorithm. It is verified that some of the existing techniques are special cases of the new scheme. The algorithms are tested in several real-life problems to check their accuracy and applicability. The results of the dynamical study confirm that the new methods are more stable and accurate than the existing schemes.</description><identifier>ISSN: 2073-8994</identifier><identifier>EISSN: 2073-8994</identifier><identifier>DOI: 10.3390/sym11070837</identifier><language>eng</language><publisher>Basel: MDPI AG</publisher><subject>Algorithms ; Convergence ; Global positioning systems ; GPS ; multiple roots ; Neighborhoods ; Nonlinear equations ; optimal iterative methods ; order of convergence ; scalar equations ; Weighting functions</subject><ispartof>Symmetry (Basel), 2019-07, Vol.11 (7), p.837</ispartof><rights>2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c364t-97f3403d8fedabe86017ba6a7aaec56484fbdadce22addb5d2164e98f5e270a43</citedby><cites>FETCH-LOGICAL-c364t-97f3403d8fedabe86017ba6a7aaec56484fbdadce22addb5d2164e98f5e270a43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/2550259205/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2550259205?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,25753,27924,27925,37012,44590,75126</link.rule.ids></links><search><creatorcontrib>Alharbey, R. A.</creatorcontrib><creatorcontrib>Kansal, Munish</creatorcontrib><creatorcontrib>Behl, Ramandeep</creatorcontrib><creatorcontrib>Machado, J. A. Tenreiro</creatorcontrib><title>Efficient Three-Step Class of Eighth-Order Multiple Root Solvers and Their Dynamics</title><title>Symmetry (Basel)</title><description>This article proposes a wide general class of optimal eighth-order techniques for approximating multiple zeros of scalar nonlinear equations. The new strategy adopts a weight function with an approach involving the function-to-function ratio. An extensive convergence analysis is performed for the eighth-order convergence of the algorithm. It is verified that some of the existing techniques are special cases of the new scheme. The algorithms are tested in several real-life problems to check their accuracy and applicability. The results of the dynamical study confirm that the new methods are more stable and accurate than the existing schemes.</description><subject>Algorithms</subject><subject>Convergence</subject><subject>Global positioning systems</subject><subject>GPS</subject><subject>multiple roots</subject><subject>Neighborhoods</subject><subject>Nonlinear equations</subject><subject>optimal iterative methods</subject><subject>order of convergence</subject><subject>scalar equations</subject><subject>Weighting functions</subject><issn>2073-8994</issn><issn>2073-8994</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNpNkU9Lw0AQxYMoWLQnv8CCR4lu9k-yOUqtWqgUbD0vk-xsuyXNxt1U6Lc3WpHOZYbhze8NvCS5yeg95yV9iIddltGCKl6cJSNGC56qshTnJ_NlMo5xS4eSVIqcjpLl1FpXO2x7stoExHTZY0cmDcRIvCVTt970m3QRDAbytm961zVI3r3vydI3XxgigdYMp-gCeTq0sHN1vE4uLDQRx3_9Kvl4nq4mr-l88TKbPM7TmueiT8vCckG5URYNVKhymhUV5FAAYC1zoYStDJgaGQNjKmlYlgsslZXICgqCXyWzI9d42OouuB2Eg_bg9O_Ch7WG0Lu6Qc1qrCwDZBa4yJlSRhiEglNaZYpLGFi3R1YX_OceY6-3fh_a4X3NpKRMlozKQXV3VNXBxxjQ_rtmVP-EoE9C4N84knnx</recordid><startdate>20190701</startdate><enddate>20190701</enddate><creator>Alharbey, R. A.</creator><creator>Kansal, Munish</creator><creator>Behl, Ramandeep</creator><creator>Machado, J. A. Tenreiro</creator><general>MDPI AG</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SR</scope><scope>7U5</scope><scope>8BQ</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>JG9</scope><scope>JQ2</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>DOA</scope></search><sort><creationdate>20190701</creationdate><title>Efficient Three-Step Class of Eighth-Order Multiple Root Solvers and Their Dynamics</title><author>Alharbey, R. A. ; Kansal, Munish ; Behl, Ramandeep ; Machado, J. A. Tenreiro</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c364t-97f3403d8fedabe86017ba6a7aaec56484fbdadce22addb5d2164e98f5e270a43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algorithms</topic><topic>Convergence</topic><topic>Global positioning systems</topic><topic>GPS</topic><topic>multiple roots</topic><topic>Neighborhoods</topic><topic>Nonlinear equations</topic><topic>optimal iterative methods</topic><topic>order of convergence</topic><topic>scalar equations</topic><topic>Weighting functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Alharbey, R. A.</creatorcontrib><creatorcontrib>Kansal, Munish</creatorcontrib><creatorcontrib>Behl, Ramandeep</creatorcontrib><creatorcontrib>Machado, J. A. Tenreiro</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Engineering Database</collection><collection>Access via ProQuest (Open Access)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection><collection>Directory of Open Access Journals</collection><jtitle>Symmetry (Basel)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Alharbey, R. A.</au><au>Kansal, Munish</au><au>Behl, Ramandeep</au><au>Machado, J. A. Tenreiro</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Efficient Three-Step Class of Eighth-Order Multiple Root Solvers and Their Dynamics</atitle><jtitle>Symmetry (Basel)</jtitle><date>2019-07-01</date><risdate>2019</risdate><volume>11</volume><issue>7</issue><spage>837</spage><pages>837-</pages><issn>2073-8994</issn><eissn>2073-8994</eissn><abstract>This article proposes a wide general class of optimal eighth-order techniques for approximating multiple zeros of scalar nonlinear equations. The new strategy adopts a weight function with an approach involving the function-to-function ratio. An extensive convergence analysis is performed for the eighth-order convergence of the algorithm. It is verified that some of the existing techniques are special cases of the new scheme. The algorithms are tested in several real-life problems to check their accuracy and applicability. The results of the dynamical study confirm that the new methods are more stable and accurate than the existing schemes.</abstract><cop>Basel</cop><pub>MDPI AG</pub><doi>10.3390/sym11070837</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 2073-8994
ispartof Symmetry (Basel), 2019-07, Vol.11 (7), p.837
issn 2073-8994
2073-8994
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_2cebf2ae2fa346288d4dea7300b1835a
source Access via ProQuest (Open Access)
subjects Algorithms
Convergence
Global positioning systems
GPS
multiple roots
Neighborhoods
Nonlinear equations
optimal iterative methods
order of convergence
scalar equations
Weighting functions
title Efficient Three-Step Class of Eighth-Order Multiple Root Solvers and Their Dynamics
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T07%3A10%3A13IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_doaj_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Efficient%20Three-Step%20Class%20of%20Eighth-Order%20Multiple%20Root%20Solvers%20and%20Their%20Dynamics&rft.jtitle=Symmetry%20(Basel)&rft.au=Alharbey,%20R.%20A.&rft.date=2019-07-01&rft.volume=11&rft.issue=7&rft.spage=837&rft.pages=837-&rft.issn=2073-8994&rft.eissn=2073-8994&rft_id=info:doi/10.3390/sym11070837&rft_dat=%3Cproquest_doaj_%3E2550259205%3C/proquest_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c364t-97f3403d8fedabe86017ba6a7aaec56484fbdadce22addb5d2164e98f5e270a43%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2550259205&rft_id=info:pmid/&rfr_iscdi=true