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Verified computation for the matrix Lambert W function

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  • Miyajima, Shinya

Abstract

Two iterative algorithms are proposed for numerically computing interval matrices containing primary matrix Lambert W functions. The first algorithm is based on a numerical spectral decomposition and involves only cubic complexity per iteration. The second algorithm is based on a numerical Jordan decomposition and applicable even for defective matrices. Numerical results show the effectiveness and robustness of the algorithms.

Suggested Citation

  • Miyajima, Shinya, 2019. "Verified computation for the matrix Lambert W function," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
  • Handle: RePEc:eee:apmaco:v:362:y:2019:i:c:9
    DOI: 10.1016/j.amc.2019.06.069
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    Cited by:

    1. Miyajima, Shinya, 2023. "Fast verified computation for real powers of large matrices with Kronecker structure," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    2. Lóczi, Lajos, 2022. "Guaranteed- and high-precision evaluation of the Lambert W function," Applied Mathematics and Computation, Elsevier, vol. 433(C).

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