A Cost-Efficient Variant of the Incremental Newton Iteration for the Matrix $p$th Root |
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| Authors: | Fuminori TATSUOKA Tomohiro SOGABE Yuto MIYATAKE and Shaoliang ZHANG |
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| Institution: | Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan,Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan,Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan and 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. |
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| Keywords: | matrix $p$th root matrix polynomial |
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