An Extended Multistep Shanks Transformation and Convergence Acceleration Algorithm with Their Convergence and Stability Analysis
An Extended Multistep Shanks Transformation and Convergence Acceleration Algorithm with Their Convergence and Stability Analysis
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DOI：
10.1007/s00211-013-0549-1
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发表时间：
2013-12
影响因子：
2.1
通讯作者：
Jianqing Sun;Xiang-Ke Chang;Yi He;Xing-Biao Hu
中科院分区：
文献类型：
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作者：
Jianqing Sun;Xiang-Ke Chang;Yi He;Xing-Biao Hu
构造了扩展离散 Lotka-Volterra 方程的分子解，并由此提出了新的序列变换。找到了实现该序列变换的收敛加速算法。结果表明，我们的新序列变换加速了某些类型的线性收敛序列和阶乘收敛序列，并具有良好的数值稳定性。还提供了一些数值示例。
The molecule solution of an extended discrete Lotka–Volterra 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.