An effective matrix geometric mean satisfying the Ando-Li-Mathias properties
An effective matrix geometric mean satisfying the Ando-Li-Mathias properties
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满足Ando-Li-Mathias性质的有效矩阵几何平均值
DOI：
10.1090/s0025-5718-09-02261-3
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Federico Poloni
中科院分区：
文献类型：
--
作者：
Dario Bini;B. Meini;Federico Poloni
我们提出了一个新的矩阵几何平均满足Ando，Li和Mathias（Linear Alg. Appl.2004]。这意味着是一个序列的极限收敛超线性收敛的顺序3，而平均介绍了安藤，李和马蒂亚斯是一个序列的极限顺序收敛1。这使得这个新的平均值非常容易计算。我们提供了一个几何解释和推广，其中包括作为特殊情况下，我们的意思和安多-李-马蒂亚斯平均。
We propose a new matrix geometric mean satisfying the ten properties given by Ando, Li and Mathias (Linear Alg. Appl. 2004]. This mean is the limit of a sequence which converges superlinearly with convergence of order 3 whereas the mean introduced by Ando, Li and Mathias is the limit of a sequence having order of convergence 1. This makes this new mean very easily computable. We provide a geometric interpretation and a generalization which includes as special cases our mean and the Ando-Li-Mathias mean.