English

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

Numerical Analysis 2019-01-07 v2

Abstract

Incremental Newton (IN) iteration, proposed by Iannazzo, is stable for computing the matrix ppth root, and its computational cost is O(n3p)\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 O(n3logp)\mathcal{O} (n^3 \log p) flops per iteration, if pp is up to at least 100.

Keywords

Cite

@article{arxiv.1611.02848,
  title  = {A cost-efficient variant of the incremental Newton iteration for the matrix $p$th root},
  author = {Fuminori Tatsuoka and Tomohiro Sogabe and Yuto Miyatake and Shao-Liang Zhang},
  journal= {arXiv preprint arXiv:1611.02848},
  year   = {2019}
}