{"title":"SINGULAR PERTURBATIONS ARISING IN COMPLEX NEWTON'S METHOD","authors":"Fi̇gen Çi̇li̇ngi̇r","doi":"10.15672/hujms.1132257","DOIUrl":null,"url":null,"abstract":"We examine the resulting dynamics when Newton's method is applied to perturbations of polynomials that have a multiple root. Specifically, we consider the case where Newton's method is applied to the polynomial family $(z^2 + c)(z-1)$.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hacettepe Journal of Mathematics and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.15672/hujms.1132257","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
We examine the resulting dynamics when Newton's method is applied to perturbations of polynomials that have a multiple root. Specifically, we consider the case where Newton's method is applied to the polynomial family $(z^2 + c)(z-1)$.
期刊介绍：
Hacettepe Journal of Mathematics and Statistics covers all aspects of Mathematics and Statistics. Papers on the interface between Mathematics and Statistics are particularly welcome, including applications to Physics, Actuarial Sciences, Finance and Economics.
We strongly encourage submissions for Statistics Section including current and important real world examples across a wide range of disciplines. Papers have innovations of statistical methodology are highly welcome. Purely theoretical papers may be considered only if they include popular real world applications.
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