极限2-周期连分式的一种新算法  

A new algorithm of limit 2-periodic continued fractions

作　　者：胡翔[1,2] 唐烁[2] 李强[2] 

机构地区：[1]安庆师范学院数学与计算科学学院,安徽安庆246011 [2]合肥工业大学数学系,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2008年第11期1900-1903,共4页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省教育厅重点资助项目(KJ2008A027)

摘　　要：加速收敛在连分式理论中占有重要的地位,对连分式进行加速收敛最常用的方法是选择合适的修正因子。如果连分式是极限k-周期的,则修正因子序列也应是k-周期的,这就使对于k≥2的周期连分式其修正因子的选取较为困难;文章借助了连分式的压缩技术,针对极限2-周期连分式推导出一种新算法,使修正因子的选取变得简单;数值例子表明新算法使连分式的收敛更快、精度更高。Convergence acceleration is important in the theory of continued fractions. Value may often be determined more quickly by using modifying factors. If the continued fraction is limit k-periodic, a natural choice for the modifying factors is a k-periodic sequence. ＇Clearly, the difficulty is to find suitable modifying factors when period k≥2. A new approach to computing the limit 2-periodic continued fractions is given by means of the property of contractions. The choosing of modifying factors will become easy by use of the new algorithm. An example is given to illustrate the validity of the new algo-rithm.

关 键 词：极限2-周期连分式 压缩 等价变换 

分 类 号：O242.2[理学—计算数学]