Provably monotone approximations

C. Dunham
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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.
可证明的单调近似
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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