{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:59Z","timestamp":1740134579983,"version":"3.37.3"},"reference-count":41,"publisher":"Wiley","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>A new iterative method for polynomial root-finding based on the development of two novel recursive functions is proposed. In addition, the concept of<jats:italic>polynomial pivots<\/jats:italic>associated with these functions is introduced. The pivots present the property of lying close to some of the roots under certain conditions; this closeness leads us to propose them as efficient starting points for the proposed iterative sequences. Conditions for local convergence are studied demonstrating that the new recursive sequences converge with linear velocity. Furthermore, an a<jats:italic>priori<\/jats:italic>checkable global convergence test inside pivots-centered balls is proposed. In order to accelerate the convergence from linear to quadratic velocity, new recursive functions together with their associated sequences are constructed. Both the recursive functions (linear) and the corrected (quadratic convergence) are validated with two nontrivial numerical examples. In them, the efficiency of the pivots as starting points, the quadratic convergence of the proposed functions, and the validity of the theoretical results are visualized.<\/jats:p>","DOI":"10.1155\/2015\/413816","type":"journal-article","created":{"date-parts":[[2015,3,23]],"date-time":"2015-03-23T17:07:32Z","timestamp":1427130452000},"page":"1-14","source":"Crossref","is-referenced-by-count":0,"title":["The Polynomial Pivots as Initial Values for a New Root-Finding Iterative Method"],"prefix":"10.1155","volume":"2015","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4949-8295","authenticated-orcid":true,"given":"Mario","family":"L\u00e1zaro","sequence":"first","affiliation":[{"name":"Department of Continuum Mechanics and Theory of Structures, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pedro","family":"Mart\u00edn","sequence":"additional","affiliation":[{"name":"Department of Continuum Mechanics and Theory of Structures, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7046-3014","authenticated-orcid":true,"given":"Antonio","family":"Ag\u00fcero","sequence":"additional","affiliation":[{"name":"Department of Continuum Mechanics and Theory of Structures, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ignacio","family":"Ferrer","sequence":"additional","affiliation":[{"name":"Department of Continuum Mechanics and Theory of Structures, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"year":"1964","key":"1"},{"year":"1973","key":"2"},{"year":"1980","key":"3"},{"year":"1993","key":"4"},{"year":"1995","key":"5"},{"year":"2007","key":"6"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(93)90064-I"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(96)00147-1"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(99)00273-3"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(01)00546-5"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(96)00080-6"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1137\/s0036144595288554"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.2002.0531"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2010.12.070"},{"year":"1998","key":"15"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1145\/365559.365619"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1007\/s002220100149"},{"key":"18","first-page":"195","volume":"17","year":"2004","journal-title":"Electronic Transactions on Numerical Analysis"},{"issue":"10","key":"19","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/S0898-1221(97)00206-X","volume":"34","year":"1997","journal-title":"Computers and Mathematics with Applications"},{"issue":"2","key":"20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0898-1221(98)00111-4","volume":"36","year":"1998","journal-title":"Computers and Mathematics with Applications"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2005.10.013"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1007\/bf01396176"},{"issue":"1","key":"23","first-page":"29","volume":"6","year":"2012","journal-title":"Malaysian Journal of Mathematical Sciences"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/709832"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1090\/s0273-0979-1981-14858-8"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1016\/s0377-0427(00)00620-8"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2006.04.039"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1016\/s0898-1221(03)90028-9"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2003.08.070"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(03)00599-X"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.09.011"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2012.09.026"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2005.09.056"},{"key":"34","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(95)00031-9"},{"key":"35","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/167927"},{"year":"2012","key":"36"},{"issue":"3","key":"37","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1017\/S0013091500008786","volume":"14","year":"1965","journal-title":"Proceedings of the Edinburgh Mathematical Society Series II"},{"year":"2001","key":"38"},{"issue":"1","key":"39","first-page":"64","volume":"16","year":"1933","journal-title":"Scandinavian Actuarial Journal"},{"key":"40","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.11.015"},{"key":"41","first-page":"61","volume-title":"A fixed point theorem for holomorphic mappings","volume":"16","year":"1968"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/413816.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/413816.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/413816.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,23]],"date-time":"2017-06-23T03:52:16Z","timestamp":1498189936000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2015\/413816\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":41,"alternative-id":["413816","413816"],"URL":"https:\/\/doi.org\/10.1155\/2015\/413816","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2015]]}}}