Worpitzky's Theorem on continued fractions

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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.

论文关键词:Continued fractions,Worpitzky

论文评审过程:Received 11 July 1999, Revised 26 January 2000, Available online 29 May 2001.

论文官网地址:https://doi.org/10.1016/S0377-0427(00)00318-6