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
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Fund Project:Supported by JSPS KAKENHI (Grant No.26286088). |
Author Name | Affiliation | 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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