无穷序列加速收敛的一个方法

A Method of Accelerating Convergence for Infinite Sequence

该文通过研究无穷序列加速收敛方法 ,在 L evin t-变换的基础上 ,考虑了L evin t-变换的迭代过程 ,提出了 L evin t-变换迭代法 ,指出了这种方法能加快序列的收敛速度 ,给出了理论证明 ,并且通过具体实例给予了证实。同时 ,此法形成了循环加速的过程 ,适合于在计算机上进行计算 ,从而在实际应用中具有明显的优越性。对于交错级数部分和序列的加速收敛 。

In this paper,with the method of accelerating convergence of infinite sequence,based on L evin t- transform and its iterative process,the iteration method of L evin- ttransform is presented.Itis pointed out that this method can increase the rate of convergence of sequence,and it is confirmed by the specific examples.At the same time, this method forms a procedure ofsuccessive acceleration,and itis applicable forcomputing in computer.The method offers obvious advantages in practical use,especially in accelerating convergence of alterating series sequences.