{"title":"An /spl epsiv/ arithmetic for removing degeneracies","authors":"D. Michelucci","doi":"10.1109/ARITH.1995.465353","DOIUrl":null,"url":null,"abstract":"Symbolic perturbation by infinitely small values removes degeneracies in geometric algorithms and enables programmers to handle only generic cases: there are a few such cases, whereas there are an overwhelming number of degenerate cases. Current perturbation schemes have limitations. To overcome them, the paper proposes to use an /spl epsiv/-arithmetic, i.e. to represent in an explicit way infinitely small numbers and to define arithmetic operations (+,-,*,/,<,=) on them.<<ETX>>","PeriodicalId":332829,"journal":{"name":"Proceedings of the 12th Symposium on Computer Arithmetic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1995-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 12th Symposium on Computer Arithmetic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.1995.465353","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
Symbolic perturbation by infinitely small values removes degeneracies in geometric algorithms and enables programmers to handle only generic cases: there are a few such cases, whereas there are an overwhelming number of degenerate cases. Current perturbation schemes have limitations. To overcome them, the paper proposes to use an /spl epsiv/-arithmetic, i.e. to represent in an explicit way infinitely small numbers and to define arithmetic operations (+,-,*,/,<,=) on them.<>
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