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.

引用

页码：143 / 148

页数：6

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