Transactions of the Japan Society for Industrial and Applied Mathematics
Online ISSN : 2424-0982
ISSN-L : 0917-2246
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  • Shinsuke Nakamura
    2023 Volume 33 Issue 4 Pages 149-177
    Published: 2023
    Released on J-STAGE: December 25, 2023

    Abstract. Logarithms of matrices defined as inverse function of exponentials of matrices arise in control theory and others. One of the algorithm that evaluate the logarithm called inverse scaling and squaring is constructed with matrix square root and Padé approximants, In this algorithm, product form DB iteration that is a variation of Newton’s method is applied to matrix square root. However, the algorithm may cause significant digit loss. So in this article, we propose a new iteration based on product form DB iteration to avoid the significant digit loss, and show the results of numerical experiments to compare their iterations.

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