{"title":"Computing parameter planes of iterative root-finding methods with several free critical points","authors":"Beatriz Campos , Jordi Canela , Alberto Rodríguez-Arenas , Pura Vindel","doi":"10.1016/j.matcom.2024.08.013","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we present an algorithm to obtain the parameter planes of families of root-finding methods with several free critical points. The parameter planes show the joint behaviour of all critical points. This algorithm avoids the inconsistencies arising from the relationship between the different critical points as well as the indeterminacy caused by the square roots involved in their computation.</p><p>We analyse the suitability of this algorithm by drawing the parameter planes of different Newton-like methods with two and three critical points. We also present some results of the expressions of the Newton-like operators and their derivatives in terms of palindromic polynomials, and we show how to obtain the expression of the critical points of a Newton-like method with real coefficients.</p></div>","PeriodicalId":4,"journal":{"name":"ACS Applied Energy Materials","volume":null,"pages":null},"PeriodicalIF":5.4000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S037847542400315X/pdfft?md5=4956d6bd6975a5a866e9fd44c4e853f4&pid=1-s2.0-S037847542400315X-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Energy Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S037847542400315X","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper we present an algorithm to obtain the parameter planes of families of root-finding methods with several free critical points. The parameter planes show the joint behaviour of all critical points. This algorithm avoids the inconsistencies arising from the relationship between the different critical points as well as the indeterminacy caused by the square roots involved in their computation.
We analyse the suitability of this algorithm by drawing the parameter planes of different Newton-like methods with two and three critical points. We also present some results of the expressions of the Newton-like operators and their derivatives in terms of palindromic polynomials, and we show how to obtain the expression of the critical points of a Newton-like method with real coefficients.
期刊介绍：
ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.
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