利用压缩变换求极限2-周期连分式的值

加速收敛在连分式理论中占有重要的地位，对极限周期连分式进行加速收敛最常用的方法是通过选择合适的修正因子。如果b0＋^∞K（n=1）（an/bn）是极限κ-周期连分式，则修正因子序列也应是κ-周期的，这就使得对于k≥2的周期连分式的修正因子的选取较为困难。借助连分式的压缩性质，针对极限2-周期连分式推导出一种新算法，从而避免修正因子的选取，数值例子表明新算法使得连分式的收敛更快，精度更高。

Computing the Value of Limit 2-Periodic Continued Fractions by Compression Transformations

Accelerated convergence is important in the theory of continued fractions in which the value may often be determined more quickly by using modifying factors.If b_o +sum from n=1 to∞(a_n/b_n) 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 compute the limit 2—periodic continued fractions is given by means of the property of compressions, which can avoid to choose some modifying factors.At last,an example is given to illustrate the validity of the new algorithm.