| Fuminori TATSUOKA,Tomohiro SOGABE,Yuto MIYATAKE,Shaoliang ZHANG.A Cost-Efficient Variant of the Incremental Newton Iteration for the Matrix $p$th Root[J].数学研究及应用,2017,37(1):97~106 |
| A Cost-Efficient Variant of the Incremental Newton Iteration for the Matrix $p$th Root |
| A Cost-Efficient Variant of the Incremental Newton Iteration for the Matrix $p$th Root |
| 投稿时间：2016-10-31 修订日期：2016-12-07 |
| DOI：10.3770/j.issn:2095-2651.2017.01.009 |
| 中文关键词: matrix $p$th root matrix polynomial |
| 英文关键词:matrix $p$th root matrix polynomial |
| 基金项目:Supported by JSPS KAKENHI (Grant No.26286088). |
| 作者 | 单位 | | 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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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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. |
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