{"title":"基于Barnett定理的多元近似GCD计算","authors":"Masaru Sanuki","doi":"10.1145/1577190.1577214","DOIUrl":null,"url":null,"abstract":"We present algorithms for multivariate GCD and approximate GCD by modifying Barnett's theorem, which is based on the LU-decomposition of Bézout matrix. Our method is suited for multivariate polynomials with large degrees. Also, we analyze ill-conditioned cases of our method. We show our method is stabler and faster than many other methods.","PeriodicalId":308716,"journal":{"name":"Symbolic-Numeric Computation","volume":"70 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Computing multivariate approximate GCD based on Barnett's theorem\",\"authors\":\"Masaru Sanuki\",\"doi\":\"10.1145/1577190.1577214\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present algorithms for multivariate GCD and approximate GCD by modifying Barnett's theorem, which is based on the LU-decomposition of Bézout matrix. Our method is suited for multivariate polynomials with large degrees. Also, we analyze ill-conditioned cases of our method. We show our method is stabler and faster than many other methods.\",\"PeriodicalId\":308716,\"journal\":{\"name\":\"Symbolic-Numeric Computation\",\"volume\":\"70 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-08-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symbolic-Numeric Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/1577190.1577214\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symbolic-Numeric Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1577190.1577214","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Computing multivariate approximate GCD based on Barnett's theorem
We present algorithms for multivariate GCD and approximate GCD by modifying Barnett's theorem, which is based on the LU-decomposition of Bézout matrix. Our method is suited for multivariate polynomials with large degrees. Also, we analyze ill-conditioned cases of our method. We show our method is stabler and faster than many other methods.
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