{"title":"一类求解无导数非线性方程的最优八阶迭代法","authors":"Laila A. Alnaser","doi":"10.37418/amsj.12.2.7","DOIUrl":null,"url":null,"abstract":"The objective of this paper is to develop new class of optimal iterative methods that do not need any derivative evaluations for solving nonlinear equations. Those new methods consist of an approximation of the eighth order and require four function evaluations per iteration which support the Kung-Traub assumption on optimal order for without memory schemes. Lastly, to show those new methods' performance and effectiveness, they are compared numerically with other similar methods in high-precision computation.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"142 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A CLASS OF OPTIMAL EIGHTH ORDER ITERATIVE METHODS FOR SOLVING NONLINEAR EQUATIONS WITHOUT DERIVATIVES\",\"authors\":\"Laila A. Alnaser\",\"doi\":\"10.37418/amsj.12.2.7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The objective of this paper is to develop new class of optimal iterative methods that do not need any derivative evaluations for solving nonlinear equations. Those new methods consist of an approximation of the eighth order and require four function evaluations per iteration which support the Kung-Traub assumption on optimal order for without memory schemes. Lastly, to show those new methods' performance and effectiveness, they are compared numerically with other similar methods in high-precision computation.\",\"PeriodicalId\":231117,\"journal\":{\"name\":\"Advances in Mathematics: Scientific Journal\",\"volume\":\"142 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-02-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematics: Scientific Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37418/amsj.12.2.7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics: Scientific Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37418/amsj.12.2.7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A CLASS OF OPTIMAL EIGHTH ORDER ITERATIVE METHODS FOR SOLVING NONLINEAR EQUATIONS WITHOUT DERIVATIVES
The objective of this paper is to develop new class of optimal iterative methods that do not need any derivative evaluations for solving nonlinear equations. Those new methods consist of an approximation of the eighth order and require four function evaluations per iteration which support the Kung-Traub assumption on optimal order for without memory schemes. Lastly, to show those new methods' performance and effectiveness, they are compared numerically with other similar methods in high-precision computation.
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