{"title":"Banach空间中变形哈雷法的改进局部分析","authors":"Debasis Sharma, S. K. Parhi, S. K. Sunanda","doi":"10.46753/pjaa.2020.v07i02.007","DOIUrl":null,"url":null,"abstract":"In this paper, we provide an improved local analysis of deformed Halley method using Hölder continuous first-order Fréchet derivative in Banach spaces. This analysis avoids the use of the extra assumption on the boundedness of the first derivative. Finally, numerical applications confirm that our analysis provides larger convergence radii in comparison with the earlier study.","PeriodicalId":37079,"journal":{"name":"Poincare Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An improved local analysis of deformed Halley method in Banach spaces\",\"authors\":\"Debasis Sharma, S. K. Parhi, S. K. Sunanda\",\"doi\":\"10.46753/pjaa.2020.v07i02.007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we provide an improved local analysis of deformed Halley method using Hölder continuous first-order Fréchet derivative in Banach spaces. This analysis avoids the use of the extra assumption on the boundedness of the first derivative. Finally, numerical applications confirm that our analysis provides larger convergence radii in comparison with the earlier study.\",\"PeriodicalId\":37079,\"journal\":{\"name\":\"Poincare Journal of Analysis and Applications\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-12-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Poincare Journal of Analysis and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46753/pjaa.2020.v07i02.007\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Poincare Journal of Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46753/pjaa.2020.v07i02.007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An improved local analysis of deformed Halley method in Banach spaces
In this paper, we provide an improved local analysis of deformed Halley method using Hölder continuous first-order Fréchet derivative in Banach spaces. This analysis avoids the use of the extra assumption on the boundedness of the first derivative. Finally, numerical applications confirm that our analysis provides larger convergence radii in comparison with the earlier study.
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