Chansangiam, Pattrawut

Preferred name

Alternative Name

Chansangiam, P.

Main Affiliation

School of Science

pattrawut.ch@kmitl.ac.th

Now showing 1 - 10 of 10

Some of the metrics are blocked by your
consent settings
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.
Some of the metrics are blocked by your
consent settings
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.
Some of the metrics are blocked by your
consent settings
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.
Some of the metrics are blocked by your
consent settings
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.
Some of the metrics are blocked by your
consent settings
Modified jacobi-gradient iterative method for generalized sylvester matrix equation
(2020-11-01)
Sasaki, Nopparut
;
Chansangiam, Pattrawut
We propose a new iterative method for solving a generalized Sylvester matrix equation A<inf>1</inf> XA<inf>2</inf> + A<inf>3</inf> XA<inf>4</inf> = E with given square matrices A<inf>1</inf>, A<inf>2</inf>, A<inf>3</inf>, A<inf>4</inf> and an unknown rectangular matrix X. The method aims to construct a sequence of approximated solutions converging to the exact solution, no matter the initial value is. We decompose the coefficient matrices to be the sum of its diagonal part and others. The recursive formula for the iteration is derived from the gradients of quadratic norm-error functions, together with the hierarchical identification principle. We find equivalent conditions on a convergent factor, relied on eigenvalues of the associated iteration matrix, so that the method is applicable as desired. The convergence rate and error estimation of the method are governed by the spectral norm of the related iteration matrix. Furthermore, we illustrate numerical examples of the proposed method to show its capability and efficacy, compared to recent gradient-based iterative methods.
Some of the metrics are blocked by your
consent settings
Convergence analysis of gradient-based iterative algorithms for a class of rectangular Sylvester matrix equations based on Banach contraction principle
(2021-12-01)
Kittisopaporn, Adisorn
;
Chansangiam, Pattrawut
;
Lewkeeratiyutkul, Wicharn
We derive an iterative procedure for solving a generalized Sylvester matrix equation AXB+ CXD= E, where A, B, C, D, E are conforming rectangular matrices. Our algorithm is based on gradients and hierarchical identification principle. We convert the matrix iteration process to a first-order linear difference vector equation with matrix coefficient. The Banach contraction principle reveals that the sequence of approximated solutions converges to the exact solution for any initial matrix if and only if the convergence factor belongs to an open interval. The contraction principle also gives the convergence rate and the error analysis, governed by the spectral radius of the associated iteration matrix. We obtain the fastest convergence factor so that the spectral radius of the iteration matrix is minimized. In particular, we obtain iterative algorithms for the matrix equation AXB= C, the Sylvester equation, and the Kalman–Yakubovich equation. We give numerical experiments of the proposed algorithm to illustrate its applicability, effectiveness, and efficiency.
Some of the metrics are blocked by your
consent settings
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.
Some of the metrics are blocked by your
consent settings
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.
Some of the metrics are blocked by your
consent settings
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.
Some of the metrics are blocked by your
consent settings
Convergence analysis of a gradient iterative algorithm with optimal convergence factor for a generalized sylvester-transpose matrix equation
(2021-01-01)
Boonruangkan, Nunthakarn
;
Chansangiam, Pattrawut
Consider a generalized Sylvester-transpose matrix equation with rectangular coefficient matrices. Based on gradients and hierarchical identification principle, we derive an iterative algorithm to produce a sequence of approximated solutions with a reasonable stopping rule concerning a relative norm-error. A convergence analysis via Banach fixed-point theorem reveals the sequence converges to a unique solution of the matrix equation for any given initial matrix if and only if the convergence factor is chosen appropriately in a certain range. The performance of algorithm is theoretically analysed through the convergence rate and error estimations. The optimal convergence factor is chosen to attain the fastest asymptotic behaviour. Finally, numerical experiments are provided to illustrate the capability and efficiency of the proposed algorithm, compared to recent gradient-based iterative algorithms.

Chansangiam, Pattrawut

Filters

Settings

Sort By

Results per page