合成序列变换在极限周期连分式加速收敛中的应用

Application of composite sequence transformations in accelerating convergence of limit periodic continued fractions

文章针对极限周期连分式K n=1 ∞〔an 1〕的加速收敛因子序列引入合成序列变换,得到新的因子序列,证明了新的因子序列也是加速收敛因子序列。从定性和定量的角度来看,在一定的条件下它比合成前的加速收敛因子序列具有更多优良性质;文章还针对所构造出来的加速收敛因子,给出了误差控制,这有利于估计算法的精确性。

This paper aims to get new sequences of accelerating convergence factors by applying composite sequence transformations to some accelerating factors of limit periodic continued fractions K n=1^∞（an/1） , It can be proved that the new sequence of factors is also accelerating convergence factors andhas more advantages than that with no composition on the basis of qualitative and quantitative analysis of the convergence of the limit periodic continued fraction under some hypotheses. For the obtained accelerating factors, the paper presents the method of error control, which is beneficial to estimating the accuracy of the algorithm.