{"title":"外聚集牛顿法求解非线性方程及其应用","authors":"Marija Paunović, Dejan Ćebić, N. Ralević","doi":"10.5937/univtho10-24982","DOIUrl":null,"url":null,"abstract":"Different modified Newton’s methods are widely used in modern computational engineering science, applied mechanics, economics, optimization problems and other disciplines. On the other hand aggregation of information takes a significant place in many knowledge-based systems, where aggregation of data or values is needed. In this paper we theoretically analysed a new modification of Newton’s method based on aggregation function applied on finding multiple roots of nonlinear equations, and numerically verified theoretical results on the examples with simple and multiple roots. Numerical analysis of the proposed approach with obtained results and the related discussion are presented on examples in practice.","PeriodicalId":22896,"journal":{"name":"The University Thought - Publication in Natural Sciences","volume":"41 1","pages":"44-50"},"PeriodicalIF":0.0000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The external aggregation Newton's method for solving nonlinear equations and applications\",\"authors\":\"Marija Paunović, Dejan Ćebić, N. Ralević\",\"doi\":\"10.5937/univtho10-24982\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Different modified Newton’s methods are widely used in modern computational engineering science, applied mechanics, economics, optimization problems and other disciplines. On the other hand aggregation of information takes a significant place in many knowledge-based systems, where aggregation of data or values is needed. In this paper we theoretically analysed a new modification of Newton’s method based on aggregation function applied on finding multiple roots of nonlinear equations, and numerically verified theoretical results on the examples with simple and multiple roots. Numerical analysis of the proposed approach with obtained results and the related discussion are presented on examples in practice.\",\"PeriodicalId\":22896,\"journal\":{\"name\":\"The University Thought - Publication in Natural Sciences\",\"volume\":\"41 1\",\"pages\":\"44-50\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The University Thought - Publication in Natural Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5937/univtho10-24982\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The University Thought - Publication in Natural Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5937/univtho10-24982","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The external aggregation Newton's method for solving nonlinear equations and applications
Different modified Newton’s methods are widely used in modern computational engineering science, applied mechanics, economics, optimization problems and other disciplines. On the other hand aggregation of information takes a significant place in many knowledge-based systems, where aggregation of data or values is needed. In this paper we theoretically analysed a new modification of Newton’s method based on aggregation function applied on finding multiple roots of nonlinear equations, and numerically verified theoretical results on the examples with simple and multiple roots. Numerical analysis of the proposed approach with obtained results and the related discussion are presented on examples in practice.