{"title":"标量情况下多点迭代法的精确松弛","authors":"Serge E. Miheev","doi":"10.1109/EMISSION.2014.6893970","DOIUrl":null,"url":null,"abstract":"Based on the principle of minimality and well applicable for one-point iterative methods the exact relaxation can be adapted also to multi point ones. It accelerates and stabilizes iterative process. Simple effective algorithm to calculate exact relaxation for n-points iterative method is proposed and justified. The algorithm allows to circumvent the problem to find roots of polynomial with degree n > 2. The algorithm calculation price is easy estimated before iteration beginning. This lets a priory to specify expediency of the exact relaxation application. If n = 2 i.e. for secant method, the calculational formulas of exact relaxation are reduced.","PeriodicalId":314830,"journal":{"name":"2014 2nd 2014 2nd International Conference on Emission Electronics (ICEE)","volume":"47 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Exact relaxation of multi point iterative methods in scalar case\",\"authors\":\"Serge E. Miheev\",\"doi\":\"10.1109/EMISSION.2014.6893970\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Based on the principle of minimality and well applicable for one-point iterative methods the exact relaxation can be adapted also to multi point ones. It accelerates and stabilizes iterative process. Simple effective algorithm to calculate exact relaxation for n-points iterative method is proposed and justified. The algorithm allows to circumvent the problem to find roots of polynomial with degree n > 2. The algorithm calculation price is easy estimated before iteration beginning. This lets a priory to specify expediency of the exact relaxation application. If n = 2 i.e. for secant method, the calculational formulas of exact relaxation are reduced.\",\"PeriodicalId\":314830,\"journal\":{\"name\":\"2014 2nd 2014 2nd International Conference on Emission Electronics (ICEE)\",\"volume\":\"47 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-09-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2014 2nd 2014 2nd International Conference on Emission Electronics (ICEE)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/EMISSION.2014.6893970\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2014 2nd 2014 2nd International Conference on Emission Electronics (ICEE)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/EMISSION.2014.6893970","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Exact relaxation of multi point iterative methods in scalar case
Based on the principle of minimality and well applicable for one-point iterative methods the exact relaxation can be adapted also to multi point ones. It accelerates and stabilizes iterative process. Simple effective algorithm to calculate exact relaxation for n-points iterative method is proposed and justified. The algorithm allows to circumvent the problem to find roots of polynomial with degree n > 2. The algorithm calculation price is easy estimated before iteration beginning. This lets a priory to specify expediency of the exact relaxation application. If n = 2 i.e. for secant method, the calculational formulas of exact relaxation are reduced.