Chansangiam, Pattrawut

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Chansangiam, Pattrawut
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Chansangiam, P.
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pattrawut.ch@kmitl.ac.th

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    Item type:Publication,
    Quaternionic conjugate-gradient method for solving the matrix equation AXB=C over generalized quaternions
    (2026-10-01)
    Tansri, Kanjanaporn
    ;
    Chansangiam, Pattrawut
    ;
    Zhang, Yang
    We propose a structure-exploiting conjugate-gradient (CG)–type algorithm for solving the matrix equation AXB=C over the generalized quaternions. The proposed method is developed from an idea of operating the linear map K(X)=AXB directly on the matrix space. This enables a matrix-free Krylov subspace implementation that avoids the explicit construction of the associated large-scale Kronecker matrix. By exploiting the intrinsic component-wise structure of quaternion matrices, the procedure performs all computations through matrix–matrix multiplications, leading to significant reductions in computational complexity and memory requirements. Finite-step convergence of the algorithm is established under suitable positive-definiteness assumptions. The proposed framework naturally includes real- and complex-valued matrix equations, the Hamilton quaternion case, and other quaternion algebras as special cases. Numerical experiments confirm the efficiency, robustness, and scalability of the proposed algorithm compared with existing methods.