非线性序列变换：加速收敛和发散级数求和的计算工具
Nonlinear Sequence Transformations: Computational Tools for the Acceleration of Convergence and the Summation of Divergent Series
摘要：
收敛问题大量地出现在数学的所有分支或科学的数学处理中。序列变换是克服这类收敛问题的主要工具。他们通过将缓慢收敛或发散的输入序列$\{s_n \}_{n=0}^{\infty}$转换为另一个具有更好数值特性的序列$\{s^{\prime}_n \}_{n=0}^{\infty}$来实现这一点。Padé逼近，其中转换的部分和幂级数的双索引序列的有理函数，是最有名的序列变换，但重点的审查将是替代序列变换，为某些问题提供更好的结果比Padé逼近。
英文摘要：
Convergence problems occur abundantly in all branches of mathematics or in the mathematical treatment of the sciences. Sequence transformations are principal tools to overcome convergence problems of the kind. They accomplish this by converting a slowly converging or diverging input sequence $\{s_n \}_{n=0}^{\infty}$ into another sequence $\{s^{\prime}_n \}_{n=0}^{\infty}$ with hopefully better numerical properties. Padé approximants, which convert the partial sums of a power series to a doubly indexed sequence of rational functions, are the best known sequence transformations, but the emphasis of the review will be on alternative sequence transformations which for some problems provide better results than Padé approximants.
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