A Cost-Efficient Variant of the Incremental Newton Iteration for the Matrix $p$th Root
Received:October 31, 2016  Revised:December 07, 2016
Key Words: matrix $p$th root   matrix polynomial  
Fund Project:Supported by JSPS KAKENHI (Grant No.26286088).
Author NameAffiliation
Fuminori TATSUOKA Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan 
Tomohiro SOGABE Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan 
Yuto MIYATAKE Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan 
Shaoliang ZHANG Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan 
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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 $\Order (n^3p)$ flops per iteration. In this paper, a cost-efficient variant of IN iteration is presented. The computational cost of the variant well agrees with $\Order (n^3 \log p)$ flops per iteration, if $p$ is up to at least 100.
Citation:
DOI:10.3770/j.issn:2095-2651.2017.01.009
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