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arXiv · 1611.02848

A cost-efficient variant of the incremental Newton iteration for the matrix $p$th root

Fuminori Tatsuoka·Tomohiro Sogabe·Yuto Miyatake·Shao-Liang Zhang
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Abstract

Incremental Newton (IN) iteration, proposed by Iannazzo, is stable for computing the matrix $p$th root, and its computational cost is $\mathcal{O}(n^3p)$ flops per iteration. In this paper, a cost-efficient variant of IN iteration is presented. The computational cost of the variant well agrees with $\mathcal{O} (n^3 \log p)$ flops per iteration, if $p$ is up to at least 100.

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Fuminori Tatsuoka, Tomohiro Sogabe, Yuto Miyatake, Shao-Liang Zhang. 2016-12-28. A cost-efficient variant of the incremental Newton iteration for the matrix $p$th root. https://doi.org/10.3770/j.issn%3A2095-2651.2017.01.009

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