{"title":"基于权函数的两点八阶非线性方程求解方法","authors":"V. Torkashvand","doi":"10.33993/jnaat501-1230","DOIUrl":null,"url":null,"abstract":"In this work, we have designed a family of with-memory methods with eighth-order convergence. We have used the weight function technique. The proposed methods have three parameters. Three self-accelerating parameters are calculated in each iterative step employing only information from the current and all previous iteration. Numerical experiments are carried out to demonstrate the convergence and the e?ciency of our iterative method.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A two-point eighth-order method based on the weight function for solving nonlinear equations\",\"authors\":\"V. Torkashvand\",\"doi\":\"10.33993/jnaat501-1230\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we have designed a family of with-memory methods with eighth-order convergence. We have used the weight function technique. The proposed methods have three parameters. Three self-accelerating parameters are calculated in each iterative step employing only information from the current and all previous iteration. Numerical experiments are carried out to demonstrate the convergence and the e?ciency of our iterative method.\",\"PeriodicalId\":287022,\"journal\":{\"name\":\"Journal of Numerical Analysis and Approximation Theory\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-11-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Numerical Analysis and Approximation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33993/jnaat501-1230\",\"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 Numerical Analysis and Approximation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33993/jnaat501-1230","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A two-point eighth-order method based on the weight function for solving nonlinear equations
In this work, we have designed a family of with-memory methods with eighth-order convergence. We have used the weight function technique. The proposed methods have three parameters. Three self-accelerating parameters are calculated in each iterative step employing only information from the current and all previous iteration. Numerical experiments are carried out to demonstrate the convergence and the e?ciency of our iterative method.