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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    Least-squares solutions of generalized linear systems and the matrix equation AXB = C under the general semi-tensor products
    (2026-01-01)
    Jaiprasert, Janthip
    ;
    Phoonphiphat, Thanaphon
    ;
    Chansangiam, Pattrawut
    ;
    Zhang, Yang
    We investigate least-squares (LS) solutions of Sylvester-type matrix equations formulated via the general semi-tensor product (GSTP) of matrices. In particular, we consider generalized linear systems of the form A (Formula presented) x = B, where A and B are given rectangular matrices and x is an unknown column vector, with k denoting the GSTP that extends both the conventional matrix product and the semi-tensor product. By analyzing the derivative of the LS error associated with the equation, we show that LS solutions can be obtained by solving an equivalent linear system under the usual matrix product. Using matrix partitioning techniques, these results are further extended to several Sylvester-type equations, including A (Formula presented) X = B, X (Formula presented) A = B. and A (Formula presented) X x B = C, where X is an unknown matrix of compatible size. This framework unifies the classical and semi-tensor product cases under a generalized algebraic setting. Furthermore, we develop a gradient-descent iterative algorithm to compute approximate LS solutions efficiently. Numerical experiments confirm the convergence, capability, and effectiveness of the proposed method.
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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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    Sylvester matrix equation under the semi-tensor product of matrices
    (2022-01-01)
    Chansangiam, Pattrawut
    ;
    Sabau, Sorin V.
    We investigate the Sylvester matrix equation in which the product is given by the semi-tensor product, and all involved matrices are matrices over an arbitrary field. We discuss necessary/sufficient condition(s) for the matrix equation to have a solution or a unique solution, or infinitely many solutions. These conditions concern ranks and linear independence. Moreover, we apply a certain kind of vectorization and matrix partitioning to transform the Sylvester equation into an equivalent linear system with respect to the conventional matrix product. Our study includes the Lyapunov equation and the equation A ⋉ X = C as special cases.
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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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    Exact and least-squares solutions of a generalized Sylvester-transpose matrix equation over generalized quaternions
    (2024-01-01)
    Jaiprasert, Janthip
    ;
    Chansangiam, Pattrawut
    We have considered a generalized Sylvester-transpose matrix equation AXB + CXTD = E, where A, B,C, D, and E are given rectangular matrices over a generalized quaternion skew-field, and X is an unknown matrix. We have applied certain vectorizations and real representations to transform the matrix equation into a matrix equation over the real numbers. Thus, we have investigated a solvability condition, general exact/least-squares solutions, minimal-norm solutions, and the exact/least-squares solution closest to a given matrix. The main equation included the equation AXB = E and the Sylvester-transpose equation. Our results also covered such matrix equations over the quaternions, and quaternionic linear systems.
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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.