{"title":"求连分式展开时的舍入误差","authors":"W. B. Jones, W. J. Thron","doi":"10.1145/800182.810374","DOIUrl":null,"url":null,"abstract":"It is well known that continued fraction expansions provide a useful means for representing and computing values of functions. Expansions for many functions of mathematical analysis and physics are contained in the literature [1, 7, 9, 10]. Other expansions can be developed from a Taylor series (convergent or asymptotic) by efficient non-linear sequence algorithms [4, 5]. In addition to questions of convergence and speed of convergence of an infinite continued fraction","PeriodicalId":204185,"journal":{"name":"ACM '74","volume":"184 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Rounding error in evaluating continued fraction expansions\",\"authors\":\"W. B. Jones, W. J. Thron\",\"doi\":\"10.1145/800182.810374\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is well known that continued fraction expansions provide a useful means for representing and computing values of functions. Expansions for many functions of mathematical analysis and physics are contained in the literature [1, 7, 9, 10]. Other expansions can be developed from a Taylor series (convergent or asymptotic) by efficient non-linear sequence algorithms [4, 5]. In addition to questions of convergence and speed of convergence of an infinite continued fraction\",\"PeriodicalId\":204185,\"journal\":{\"name\":\"ACM '74\",\"volume\":\"184 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM '74\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/800182.810374\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM '74","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/800182.810374","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Rounding error in evaluating continued fraction expansions
It is well known that continued fraction expansions provide a useful means for representing and computing values of functions. Expansions for many functions of mathematical analysis and physics are contained in the literature [1, 7, 9, 10]. Other expansions can be developed from a Taylor series (convergent or asymptotic) by efficient non-linear sequence algorithms [4, 5]. In addition to questions of convergence and speed of convergence of an infinite continued fraction
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