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Singular value decomposition for complex matrices using two-sided Jacobi method

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Abstract

The two-sided Jacobi method for singular value decomposition (SVD) has the advantage of obtaining singular vectors quickly and accurately. In previous research, fast and accurate implementations of the two-sided Jacobi method have been achieved for real matrices. In this study, we implemented SVD for complex matrices using the two-sided Jacobi method. In SVD, given rectangular matrices can be converted into upper-triangular matrices by conducting QR decomposition as a preprocessing step. Then, the upper-triangular matrices are decomposed. In the case where the given matrices are complex, the upper-triangular matrices are complex. Two implementations are proposed: the first requires SVD for complex matrices, whereas the second requires SVD for only real matrices.

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Acknowledgements

This work was supported by JST SPRING, Grant Number JPMJSP2115. We would like to thank Editage (www.editage.jp) for English language editing.

Funding

JST SPRING, Grant Number JPMJSP2115.

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Authors and Affiliations

  1. Graduate School of Humanities and Sciences, Nara Women’s University, Kitauoya-Nishi-machi, Nara, Nara, 6308506, Japan

    Miho Chiyonobu

  2. Faculty of Engineering, University of Fukui, Bunkyo 3-9-1, Fukui, Fukui, 9100017, Japan

    Takahiro Miyamae, Jun Harayama & Kinji Kimura

  3. Research Group of Information and Communication Technology for Life, Nara Women’s University, Kitauoya-Nishi-machi, Nara, Nara, 6308506, Japan

    Masami Takata

  4. Faculty of Data Science, Osaka Seikei University, Higashi-Yodogawaku Aikawa 3-10-62, Osaka, Osaka, 5330007, Japan

    Yoshimasa Nakamura

Authors
  1. Miho Chiyonobu
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  2. Takahiro Miyamae
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  3. Masami Takata
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  4. Jun Harayama
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  5. Kinji Kimura
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  6. Yoshimasa Nakamura
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Contributions

MC, MT and KK wrote the main manuscript text. All authors reviewed the manuscript.

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Correspondence to Miho Chiyonobu or Masami Takata.

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Chiyonobu, M., Miyamae, T., Takata, M. et al. Singular value decomposition for complex matrices using two-sided Jacobi method. J Supercomput 80, 11719–11740 (2024). https://doi.org/10.1007/s11227-024-05903-6

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  • DOI: https://doi.org/10.1007/s11227-024-05903-6

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