Chansangiam, Pattrawut

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

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    Conjugate gradient algorithm for consistent generalized Sylvester-transpose matrix equations
    (2022-01-01)
    Tansri, Kanjanaporn
    ;
    Choomklang, Sarawanee
    ;
    Chansangiam, Pattrawut
    We develop an effective algorithm to find a well-approximate solution of a generalized Sylvester-transpose matrix equation where all coefficient matrices and an unknown matrix are rectangular. The algorithm aims to construct a finite sequence of approximated solutions from any given initial matrix. It turns out that the associated residual matrices are orthogonal, and thus, the desire solution comes out in the final step with a satisfactory error. We provide numerical experiments to show the capability and performance of the algorithm.
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    General solutions for descriptor systems of coupled generalized sylvester matrix fractional differential equations via canonical forms
    (2020-02-01)
    Tansri, Kanjanaporn
    ;
    Chansangiam, Pattrawut
    We investigate a descriptor system of coupled generalized Sylvester matrix fractional differential equations in both non-homogeneous and homogeneous cases. All fractional derivatives considered here are taken in Caputo's sense. We explain a 4-step procedure to solve the descriptor system, consisting of vectorization, a matrix canonical form concerning ranks, and matrix partitioning. The procedure aims to reduce the descriptor system to a descriptor system of fractional differential equations. We also impose a condition on coefficient matrices, related to the symmetry of the solution for descriptor systems. It follows that an explicit form of its general solution is given in terms of matrix power series concerning Mittag-Leffler functions. The main system includes certain systems of coupled matrix/vector differential equations, and single matrix differential equations as special cases. In particular, we obtain an alternative procedure to solve linear continuous-time descriptor systems via a matrix canonical form.
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    Conjugate Gradient Algorithm for Least-Squares Solutions of a Generalized Sylvester-Transpose Matrix Equation
    (2022-09-01)
    Tansri, Kanjanaporn
    ;
    Chansangiam, Pattrawut
    We derive a conjugate-gradient type algorithm to produce approximate least-squares (LS) solutions for an inconsistent generalized Sylvester-transpose matrix equation. The algorithm is always applicable for any given initial matrix and will arrive at an LS solution within finite steps. When the matrix equation has many LS solutions, the algorithm can search for the one with minimal Frobenius-norm. Moreover, given a matrix Y, the algorithm can find a unique LS solution closest to Y. Numerical experiments show the relevance of the algorithm for square/non-square dense/sparse matrices of medium/large sizes. The algorithm works well in both the number of iterations and the computation time, compared to the direct Kronecker linearization and well-known iterative methods.
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    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.