{"title":"理性户主转换","authors":"Ana C. Camargos Couto, D. J. Jeffrey","doi":"10.1109/SYNASC.2018.00022","DOIUrl":null,"url":null,"abstract":"This paper describes a method for generating integer matrices which, when QR-decomposed through Householder transformations, require only rational computations and give rational results. The motivation is pedagogical: we want to avoid the unnecessary complications that arise from heavy arithmetic manipulations of expressions containing square-roots in linear algebra problem sets and exams.","PeriodicalId":273805,"journal":{"name":"2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Rational Householder Transformations\",\"authors\":\"Ana C. Camargos Couto, D. J. Jeffrey\",\"doi\":\"10.1109/SYNASC.2018.00022\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper describes a method for generating integer matrices which, when QR-decomposed through Householder transformations, require only rational computations and give rational results. The motivation is pedagogical: we want to avoid the unnecessary complications that arise from heavy arithmetic manipulations of expressions containing square-roots in linear algebra problem sets and exams.\",\"PeriodicalId\":273805,\"journal\":{\"name\":\"2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SYNASC.2018.00022\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SYNASC.2018.00022","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper describes a method for generating integer matrices which, when QR-decomposed through Householder transformations, require only rational computations and give rational results. The motivation is pedagogical: we want to avoid the unnecessary complications that arise from heavy arithmetic manipulations of expressions containing square-roots in linear algebra problem sets and exams.
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