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<p>In this paper, we investigate the singular value decomposition for quaternion matrices. Building on the quaternion Lanczos algorithm and the block Golub-Kahan-Lanczos algorithm, we propose a quaternion block Golub-Kahan-Lanczos algorithm and prove its convergence. By applying the thick restart strategy, we develop a thick-restart quaternion block Golub-Kahan-Lanczos algorithm to accelerate its performance. Numerical experiments demonstrate that the proposed algorithm outperforms existing methods in both computation time and accuracy.</p>

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Block Golub-Kahan-Lanczos algorithms for quaternion singular value decomposition

  • 期刊论文

  • 发表日期：

    2026年1月24日

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  • Gengyuan Fan,
  • Hongxiu Zhong

摘要

In this paper, we investigate the singular value decomposition for quaternion matrices. Building on the quaternion Lanczos algorithm and the block Golub-Kahan-Lanczos algorithm, we propose a quaternion block Golub-Kahan-Lanczos algorithm and prove its convergence. By applying the thick restart strategy, we develop a thick-restart quaternion block Golub-Kahan-Lanczos algorithm to accelerate its performance. Numerical experiments demonstrate that the proposed algorithm outperforms existing methods in both computation time and accuracy.