{"title":"多分段法的效率","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":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":\"2024-11-02\",\"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\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","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":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们研究了单变量非线性方程的多分段法与著名的分段法相比的效率。我们的研究表明，有一种最省力的算法可以使用比分段法更多的分段，尽管这种最优算法与问题有关。最优化所需的截面数是通过兰伯特 W 函数确定的。
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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