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An extended multistep shanks transformation and convergence acceleration algorithm with their convergence and stability analysis

Jian-Qing Sun Xiang-Ke Chang Yi He Xing-Biao Hu

Dynamical Systems mathscidoc:1912.43163

Numerische Mathematik, 125, (4), 785-809, 2013.12
The molecule solution of an extended discrete LotkaVolterra equation is constructed, from which a new sequence transformation is proposed. A convergence acceleration algorithm for implementing this sequence transformation is found. It is shown that our new sequence transformation accelerates some kinds of linearly convergent sequences and factorially convergent sequences with good numerical stability. Some numerical examples are also presented.
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@inproceedings{jian-qing2013an,
  title={An extended multistep shanks transformation and convergence acceleration algorithm with their convergence and stability analysis},
  author={Jian-Qing Sun, Xiang-Ke Chang, Yi He, and Xing-Biao Hu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112656471129723},
  booktitle={Numerische Mathematik},
  volume={125},
  number={4},
  pages={785-809},
  year={2013},
}
Jian-Qing Sun, Xiang-Ke Chang, Yi He, and Xing-Biao Hu. An extended multistep shanks transformation and convergence acceleration algorithm with their convergence and stability analysis. 2013. Vol. 125. In Numerische Mathematik. pp.785-809. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112656471129723.
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