{"title":"用递归函数求解方程的kurchatov型方法的收敛性","authors":"I. Argyros, S. Shakhno, H. Yarmola","doi":"10.30970/ms.58.1.103-112","DOIUrl":null,"url":null,"abstract":"We study a local and semi-local convergence of Kurchatov's method and its two-step modification for solving nonlinear equations under the classical Lipschitz conditions for the first-order divided differences. To develop a convergence analysis we use the approach of restricted convergence regions in a combination to our technique of recurrent functions. The semi-local convergence is based on the majorizing scalar sequences. Also, the results of the numerical experiment are given.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the convergence of Kurchatov-type methods using recurrent functions for solving equations\",\"authors\":\"I. Argyros, S. Shakhno, H. Yarmola\",\"doi\":\"10.30970/ms.58.1.103-112\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study a local and semi-local convergence of Kurchatov's method and its two-step modification for solving nonlinear equations under the classical Lipschitz conditions for the first-order divided differences. To develop a convergence analysis we use the approach of restricted convergence regions in a combination to our technique of recurrent functions. The semi-local convergence is based on the majorizing scalar sequences. Also, the results of the numerical experiment are given.\",\"PeriodicalId\":37555,\"journal\":{\"name\":\"Matematychni Studii\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Matematychni Studii\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30970/ms.58.1.103-112\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Matematychni Studii","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30970/ms.58.1.103-112","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
On the convergence of Kurchatov-type methods using recurrent functions for solving equations
We study a local and semi-local convergence of Kurchatov's method and its two-step modification for solving nonlinear equations under the classical Lipschitz conditions for the first-order divided differences. To develop a convergence analysis we use the approach of restricted convergence regions in a combination to our technique of recurrent functions. The semi-local convergence is based on the majorizing scalar sequences. Also, the results of the numerical experiment are given.
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