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

DOI：10.3770/j.issn:2095-2651.2017.01.009

 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

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.

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.