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  最后修改时间: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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