极限周期连分式的一种较快加速收敛方法

A Method to Accelerate Convergence of Limit Periodic Continued Fraction

对极限周期连分式的一类修正逼近式序列进行变换以期达到快速加速的目的,并证明新的逼近式在一定条件下具有更快的加速逼近效果.最后用数值例子验证方法的可行性和有效性.

In this paper,modified approximants associated with a kind of accelerating convergence factors for limit periodic continued fraction were used to form new approximate sequences by sequence transformation.Under some conditions,the new sequences converge faster than old ones in approximation.Numerical examples showed that the method is available and efficient.