{"title":"初等函数求值误差估计的现实模型","authors":"K. Frankowski","doi":"10.1109/ARITH.1978.6155776","DOIUrl":null,"url":null,"abstract":"Floating point error analysis, as described by J. H. Wilkinson (1963) has two known drawbacks: it is too pessimistic and too cumbersome for everyday use. This paper describes a realistic model for error analysis, gives examples of simple formulae frequently used in the calculation of elementary functions, and analyses the error generated in single precision computations with these formulae, using the proposed model for error analysis. The paper also presents error bounds for various polynomial evaluations, as predicted by the model. Model verification is done using double precision arithmetic.","PeriodicalId":443215,"journal":{"name":"1978 IEEE 4th Symposium onomputer Arithmetic (ARITH)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1978-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A realistic model for error estimates in the evaluation of elementary functions\",\"authors\":\"K. Frankowski\",\"doi\":\"10.1109/ARITH.1978.6155776\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Floating point error analysis, as described by J. H. Wilkinson (1963) has two known drawbacks: it is too pessimistic and too cumbersome for everyday use. This paper describes a realistic model for error analysis, gives examples of simple formulae frequently used in the calculation of elementary functions, and analyses the error generated in single precision computations with these formulae, using the proposed model for error analysis. The paper also presents error bounds for various polynomial evaluations, as predicted by the model. Model verification is done using double precision arithmetic.\",\"PeriodicalId\":443215,\"journal\":{\"name\":\"1978 IEEE 4th Symposium onomputer Arithmetic (ARITH)\",\"volume\":\"13 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1978-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"1978 IEEE 4th Symposium onomputer Arithmetic (ARITH)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ARITH.1978.6155776\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"1978 IEEE 4th Symposium onomputer Arithmetic (ARITH)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.1978.6155776","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A realistic model for error estimates in the evaluation of elementary functions
Floating point error analysis, as described by J. H. Wilkinson (1963) has two known drawbacks: it is too pessimistic and too cumbersome for everyday use. This paper describes a realistic model for error analysis, gives examples of simple formulae frequently used in the calculation of elementary functions, and analyses the error generated in single precision computations with these formulae, using the proposed model for error analysis. The paper also presents error bounds for various polynomial evaluations, as predicted by the model. Model verification is done using double precision arithmetic.
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