Accuracy Improvement of Newton's Method for the Matrix Logarithm

DOI

Bibliographic Information

Other Title
  • 行列対数関数のためのニュートン法の精度改善

Description

<p>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.</p>

Journal

Keywords

Details 詳細情報について

  • CRID
    1390017113108660480
  • DOI
    10.11540/jsiamt.33.4_149
  • ISSN
    24240982
  • Text Lang
    ja
  • Data Source
    • JaLC
  • Abstract License Flag
    Disallowed

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