Worpitzky's Theorem on continued fractions

被引：6
|
作者：
Beardon, AF [1 ]
机构：
[1] Ctr Math Sci, Dept Pure Math, Cambridge CB3 0WB, England
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2001年 / 131卷 / 1-2期
关键词：
continued fractions; Worpitzky;
D O I：
10.1016/S0377-0427(00)00318-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is known that under the hypotheses in Worpitzky's Theorem on continued fractions, the approximants converge to the value of the continued fraction with error O(1/n), and that this estimate is best possible. Using a geometric argument we give a more refined estimate of the rate of convergence. We also extend a result of Waadeland that is closely connected to Worpitzky's Theorem. (C) 2001 Elsevier Science B.V. All rights reserved.
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页码：143 / 148
页数：6
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