{"title":"浮点运算中求多项式单根的几种精确方法","authors":"Peibing Du, Lizhi Cheng, Hao Jiang, Feicheng Wang","doi":"10.1109/ICCIS.2012.284","DOIUrl":null,"url":null,"abstract":"This paper presents three accurate methods for finding simple roots of polynomials in floating point arithmetic. We present them by using the Compensated Horner algorithm to accurately compute the residual which can yield a full precision when the problem is ill-conditioned enough. Some numerical experiments are conducted to justify the proposed approaches.","PeriodicalId":269967,"journal":{"name":"2012 Fourth International Conference on Computational and Information Sciences","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2012-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Accurate Methods for Finding Simple Roots of Polynomials in Floating Point Arithmetic\",\"authors\":\"Peibing Du, Lizhi Cheng, Hao Jiang, Feicheng Wang\",\"doi\":\"10.1109/ICCIS.2012.284\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents three accurate methods for finding simple roots of polynomials in floating point arithmetic. We present them by using the Compensated Horner algorithm to accurately compute the residual which can yield a full precision when the problem is ill-conditioned enough. Some numerical experiments are conducted to justify the proposed approaches.\",\"PeriodicalId\":269967,\"journal\":{\"name\":\"2012 Fourth International Conference on Computational and Information Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-08-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2012 Fourth International Conference on Computational and Information Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICCIS.2012.284\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 Fourth International Conference on Computational and Information Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICCIS.2012.284","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Some Accurate Methods for Finding Simple Roots of Polynomials in Floating Point Arithmetic
This paper presents three accurate methods for finding simple roots of polynomials in floating point arithmetic. We present them by using the Compensated Horner algorithm to accurately compute the residual which can yield a full precision when the problem is ill-conditioned enough. Some numerical experiments are conducted to justify the proposed approaches.
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