论文标题
替代的一致性谐波系列第2部分 - 融合加速度
The alternate congruo-harmonic series Part 2 -- Accelerations of convergence
论文作者
论文摘要
对于严格积极整数的每对（p; q），``替代的一致性 - 谐波''序列由（p; q）参数为参数，其一般术语为（-1）^k/（pk+q），infrra-linearearearearearearearearearlialearearearearlialearearearearelearearlialearearearearlialeareareleartial andereal且非常缓慢。基于该系列其余部分的一般部分扩展，本文详细阐述了一个算法，该算法加速了其收敛。比较了这些算法产生的序列的收敛速度。进行了精确的渐近分析，该分析揭示了促进融合的可能性（但具有无限的速度多样性）或线性（具有与（P; Q）相对（P; Q）相对普遍的收敛速率），或通过序列提取。还讨论了几个开放问题，这些问题涉及如此构建的算法的相对``性能''以及其中一些可能的最优性。
For every couple (p;q) of strictly positive integers, the `` alternate congruo-harmonic '' series parametrized by (p;q), whose general term is (-1)^k/(pk+q), converges infra-linearly and very slowly. On the basis of a generalized continued fraction expansion of the partial rest of the series, this paper elaborates a family of algorithms which accelerate its convergence. The convergence speed of the sequences generated by these algorithms are compared. A precise asymptotic analysis is conducted, which reveals the possibility to accelerate the convergence either infra-linearly (but with an infinite diversity of possible speeds), or linearly (with a convergence rate that appears universal relatively to (p;q)), or super-linearly, by means of sequences extractions. Several open problems are also discussed, which concern the relative `` performance '' of the algorithms thus built and the possible optimality of some of them.
