{"title":"Efficiency of the multisection method","authors":"J.S.C. Prentice","doi":"10.1016/j.jcmds.2024.100106","DOIUrl":null,"url":null,"abstract":"<div><div>We study the efficiency of the multisection method for univariate nonlinear equations, relative to that for the well-known bisection method. We show that there is a minimal effort algorithm that uses more sections than the bisection method, although this optimal algorithm is problem dependent. The number of sections required for optimality is determined by means of a Lambert <em>W</em> function.</div></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"13 ","pages":"Article 100106"},"PeriodicalIF":0.0000,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Mathematics and Data Science","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2772415824000178","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/11/2 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study the efficiency of the multisection method for univariate nonlinear equations, relative to that for the well-known bisection method. We show that there is a minimal effort algorithm that uses more sections than the bisection method, although this optimal algorithm is problem dependent. The number of sections required for optimality is determined by means of a Lambert W function.
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