{"title":"Provably monotone approximations","authors":"C. Dunham","doi":"10.1145/24936.24938","DOIUrl":null,"url":null,"abstract":"In the preceding note (Dunham, 1987) were given forms of approximation that were provably monotone for suitable arithmetic, but left open the forms(1) c + x * r (x),where r could be a rational (the Kuki form on middle p. 9) or the next to last stage in Horner's method (top p. 10). If r is positive and non-decreasing on a positive interval I, (1) is obviously monotone on I for monotone arithmetic. This leaves two cases, (a)r positive and (slowly) decreasing on I, and (b) r negative on I. We consider them separately.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"59 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1987-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Signum Newsletter","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/24936.24938","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
In the preceding note (Dunham, 1987) were given forms of approximation that were provably monotone for suitable arithmetic, but left open the forms(1) c + x * r (x),where r could be a rational (the Kuki form on middle p. 9) or the next to last stage in Horner's method (top p. 10). If r is positive and non-decreasing on a positive interval I, (1) is obviously monotone on I for monotone arithmetic. This leaves two cases, (a)r positive and (slowly) decreasing on I, and (b) r negative on I. We consider them separately.
在前面的注释中(Dunham, 1987)给出了对于合适的算法来说可以证明是单调的近似形式,但保留了(1)c + x * r (x)的形式,其中r可以是有理性的(中间第9页上的Kuki形式)或Horner方法的下一个最后阶段(第10页上)。如果r在正区间I上为正且不递减,则(1)对于单调算法在I上明显是单调的。这就留下了两种情况,(a)r在I上为正且(缓慢)减小,(b) r在I上为负,我们分别考虑它们。