A new integrable convergence acceleration algorithm for computing Brezinski-Durbin-Redivo-Zaglia's sequence transformation via pfaffians
A new integrable convergence acceleration algorithm for computing Brezinski-Durbin-Redivo-Zaglia's sequence transformation via pfaffians
复制标题
一种新的可积收敛加速算法，用于通过 pfaffians 计算 Brezinski-Durbin-Redivo-Zaglia 序列变换
DOI：
10.1007/s11075-017-0368-z
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发表时间：
2018
影响因子：
2.1
通讯作者：
Li Shi Hao
中科院分区：
文献类型：
--
作者：
Chang Xiang Ke;He Yi;Hu Xing Biao;Li Shi Hao
在文献中，大多数已知的序列变换可以写成两个行列式的比值。但是，情况并非总是如此。一个例外是，Brezinski、Durbin和Redivo-Zaglia提出的序列变换不能表示为两个行列式的比值。受此启发，本文将引入一种新的代数工具——定式，而不是行列式。结果表明，Brezinski-Durbin-Redivo-Zaglia的变换可以表示为两个pfaffians的比值。据我们所知，这是第一次在序列变换的表达式中引入算子。在此基础上，提出了一种高阶扩展变换，并构造了一种实现该变换的收敛加速算法。然后，得到了递推算法的Lax对，证明了该算法是可积的。最后给出了应用该算法的数值算例。
In the literature, most known sequence transformations can be written as a ratio of two determinants. But, it is not always this case. One exception is that the sequence transformation proposed by Brezinski, Durbin, and Redivo-Zaglia cannot be expressed as a ratio of two determinants. Motivated by this, we will introduce a new algebraic tool—pfaffians, instead of determinants in the paper. It turns out that Brezinski–Durbin–Redivo-Zaglia’s transformation can be expressed as a ratio of two pfaffians. To the best of our knowledge, this is the first time to introduce pfaffians in the expressions of sequence transformations. Furthermore, an extended transformation of high order is presented in terms of pfaffians and a new convergence acceleration algorithm for implementing the transformation is constructed. Then, the Lax pair of the recursive algorithm is obtained which implies that the algorithm is integrable. Numerical examples with applications of the algorithm are also presented.