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A Fast Projected Gradient Algorithm for Quaternion Hermitian Eigenvalue Problems

Author

Listed:
  • Shan-Qi Duan

    (Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China)

  • Qing-Wen Wang

    (Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China
    Collaborative Innovation Center for the Marine Artificial Intelligence, Shanghai University, Shanghai 200444, China)

Abstract

In this paper, based on the novel generalized Hamilton-real (GHR) calculus, we propose for the first time a quaternion Nesterov accelerated projected gradient algorithm for computing the dominant eigenvalue and eigenvector of quaternion Hermitian matrices. By introducing momentum terms and look-ahead updates, the algorithm achieves a faster convergence rate. We theoretically prove the convergence of the quaternion Nesterov accelerated projected gradient algorithm. Numerical experiments show that the proposed method outperforms the quaternion projected gradient ascent method and the traditional algebraic methods in terms of computational accuracy and runtime efficiency.

Suggested Citation

  • Shan-Qi Duan & Qing-Wen Wang, 2025. "A Fast Projected Gradient Algorithm for Quaternion Hermitian Eigenvalue Problems," Mathematics, MDPI, vol. 13(6), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:994-:d:1614940
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    References listed on IDEAS

    as
    1. Shan-Qi Duan & Qing-Wen Wang & Xue-Feng Duan, 2024. "On Rayleigh Quotient Iteration for the Dual Quaternion Hermitian Eigenvalue Problem," Mathematics, MDPI, vol. 12(24), pages 1-21, December.
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