Chansangiam, Pattrawut

Preferred name

Alternative Name

Chansangiam, P.

Main Affiliation

School of Science

pattrawut.ch@kmitl.ac.th

Now showing 1 - 10 of 31

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Weighted Lim’s geometric mean of positive invertible operators on a Hilbert space
(2020-03-01)
Ploymukda, Arnon
;
Chansangiam, Pattrawut
We generalize the weighted Lim’s geometric mean of positive definite matrices to positive invertible operators on a Hilbert space. This mean is defined via a certain bijection map and parametrized over Hermitian unitary operators. We derive an explicit formula of the weighted Lim’s geometric mean in terms of weighted metric/spectral geometric means. This kind of operator mean turns out to be a symmetric Lim-Pálfia weighted mean and satisfies the idempotency, the permutation invariance, the joint homogeneity, the self-duality, and the unitary invariance. Moreover, we obtain relations between weighted Lim geometric means and Tracy-Singh products via operator identities.
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THE GEOMETRY ON THE SLOPE OF A MOUNTAIN
(2020-01-01)
Chansri, P.
;
Chansangiam, P.
;
Sabau, Sorin V.
The geometry on a slope of a mountain is the geometry of a Finsler metric, called here the slope metric. We study the existence of globally defined slope metrics on surfaces of revolution as well as the geodesic’s behavior. A comparison between Finslerian and Riemannian areas of a bounded region is also studied.
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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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Riccati equation and metric geometric means of positive semidefinite matrices involving semi-tensor products
(2023-01-01)
Chansangiam, Pattrawut
;
Ploymukda, Arnon
We investigate the Riccati matrix equation XA<sup>−1</sup>X = B in which the conventional matrix products are generalized to the semi-tensor products ⋉. When A and B are positive definite matrices satisfying the factor-dimension condition, this equation has a unique positive definite solution, which is defined to be the metric geometric mean of A and B. We show that this geometric mean is the maximum solution of the Riccati inequality. We then extend the notion of the metric geometric mean to positive semidefinite matrices by a continuity argument and investigate its algebraic properties, order properties and analytic properties. Moreover, we establish some equations and inequalities of metric geometric means for matrices involving cancellability, positive linear map and concavity. Our results generalize the conventional metric geometric means of matrices.
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Solving the Sylvester-Transpose Matrix Equation under the Semi-Tensor Product
(2022-06-01)
Jaiprasert, Janthip
;
Chansangiam, Pattrawut
This paper investigates the Sylvester-transpose matrix equation A ⋉ X + X<sup>T</sup> ⋉ B = C, where all mentioned matrices are over an arbitrary field. Here, ⋉ is the semi-tensor product, which is a generalization of the usual matrix product defined for matrices of arbitrary dimensions. For matrices of compatible dimensions, we investigate criteria for the equation to have a solution, a unique solution, or infinitely many solutions. These conditions rely on ranks and linear dependence. Moreover, we find suitable matrix partitions so that the matrix equation can be transformed into a linear system involving the usual matrix product. Our work includes the studies of the equation A ⋉ X = C, the equation X ⋉ B = C, and the classical Sylvester-transpose matrix equation.
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Jensen’s type inequalities involving tracy-singh products, khatri-rao products, tracy-singh sums and khatri-rao sums
(2020-01-01)
Ploymukda, Arnon
;
Chansangiam, Pattrawut
In this paper, we establish a number of Jensen’s type inequalities for Hilbert space operators involving convex/concave functions, unital positive linear maps, and certain operator products and sums. The products and sums considered here include the Tracy-Singh product, the Khatri-Rao products, the Tracy-Singh sum, and the Khatri-Rao sum. Moreover, we generalize Jensen’s type inequalities in term of functional calculus of two-variable functions. In particular, we obtain Kantorovich-type operator inequalities involving the products and sums.
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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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Surfaces of revolution admitting strongly convex slope metrics
(2020-01-01)
Chansangiam, Pattrawut
;
Chansri, Pipatpong
This paper discusses the geometry of a surface endowed with a slope metric. We obtain necessary and sufficient conditions for any surface of revolution to admit a strongly convex slope metric. Such conditions involve certain inequalities for the derivative of the associated function on the Cartesian coordinate and the polar coordinate. In particular, we apply this result to a certain well-known surface of revolution.
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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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Three-saddle-foci chaotic behavior of a modified jerk circuit with chua’s diode
(2020-11-01)
Chansangiam, Pattrawut
This paper investigates the chaotic behavior of a modified jerk circuit with Chua’s diode. The Chua’s diode considered here is a nonlinear resistor having a symmetric piecewise linear voltage-current characteristic. To describe the system, we apply fundamental laws in electrical circuit theory to formulate a mathematical model in terms of a third-order (jerk) nonlinear differential equation, or equivalently, a system of three first-order differential equations. The analysis shows that this system has three collinear equilibrium points. The time waveform and the trajectories about each equilibrium point depend on its associated eigenvalues. We prove that all three equilibrium points are of type saddle focus, meaning that the trajectory of (x(t), y(t)) diverges in a spiral form but z(t) converges to the equilibrium point for any initial point (x(0), y(0), z(0)). Numerical simulation illustrates that the oscillations are dense, have no period, are highly sensitive to initial conditions, and have a chaotic hidden attractor.

Chansangiam, Pattrawut

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