{"title":"Accelerative Iterative Formula for the Non-linear Operator Equation","authors":"Suqing Hou, He Li, Kaisu Wu","doi":"10.3724/SP.J.1160.2012.00177","DOIUrl":null,"url":null,"abstract":"Approximate solving method for the non-linear operator equation is investigated in this paper.First,we generalize the accelerative iterative formula of the non-linear functional equation so that we obtain the high-speed convergent iterative formula.Finally,the new accelerative iterative formula has been generalized for the non-linear operator equation.Using the asymptotic expansions of the non-linear operator,we prove that the new accelerative iterative formula is convergence with order 3.","PeriodicalId":62008,"journal":{"name":"应用泛函分析学报","volume":"14 1","pages":"177"},"PeriodicalIF":0.0000,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"应用泛函分析学报","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.3724/SP.J.1160.2012.00177","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Approximate solving method for the non-linear operator equation is investigated in this paper.First,we generalize the accelerative iterative formula of the non-linear functional equation so that we obtain the high-speed convergent iterative formula.Finally,the new accelerative iterative formula has been generalized for the non-linear operator equation.Using the asymptotic expansions of the non-linear operator,we prove that the new accelerative iterative formula is convergence with order 3.
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