• Honam Mathematical Journal
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• v.39 no.4
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• pp.617-635
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• 2017

By applying a classical approach for scalar rational interpolation problem, certain type of minimal interpolation problem for rational matrix functions is solved. It is shown that an appropriately defined matrix plays a key role in solving the minimal problem.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.898-902
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• 2003

For linear descriptor systems, we consider the $H_{INFTY}$ controller design problem via output feedback. Both static output feedback and dynamic one are discussed. First, in the case of static output feedback, we reduce our control problem to solving a bilinear matrix inequality (BMI) with respect to the controller coefficient matrix, a Lyapunov matrix and a matrix related to the descriptor matrix. Under a matching condition between the descriptor matrix and the measured output matrix (or the control input matrix), we propose setting the Lyapunov matrix in the BMI as being block diagonal appropriately so that the BMI is reduced to LMIs. For fixed-order dynamic $H_{INFTY}$ output feedback, we formulate the control problem equivalently as the one of static output feedback design, and thus the same approach can be applied.

• Proceedings of the KIEE Conference
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• 1999.07b
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• pp.592-595
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• 1999

In this paper, we propose a unified method to solve the various robust filtering problem for a class of uncertain discrete time systems. Generally, to solve the robust filtering problem, we must convert the convex optimization problem with uncertainty blocks to the uncertainty free convex optimization problem. To do this, we derive the robust matrix inequality problem. This technique involves using constant scaling parameter which can be optimized by solving a linear matrix inequality problem. Therefore, the robust matrix inequality problem does not conservative. The robust filter can be designed by using this robust matrix inequality problem and by considering its solvability conditions.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.505-511
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• 2007

Recently, the equivalent relations between a symmetric dual problem and a matrix game B(x, y) were given in [6: D.S. Kim and K. Noh, J. Math. Anal. Appl. 298(2004), 1-13]. Using more simpler form of B(x, y) than one in [6], we establish the equivalence relations between a symmetric dual problem and a matrix game, and then give a numerical example illustrating our equivalence results.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1233-1245
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• 2008

In this paper, an iterative method is proposed to solve the least-squares problem of matrix equation AXB+CYD=E over unknown matrix pair [X, Y]. By this iterative method, for any initial matrix pair [$X_1,\;Y_1$], a solution pair or the least-norm least-squares solution pair of which can be obtained within finite iterative steps in the absence of roundoff errors. In addition, we also consider the optimal approximation problem for the given matrix pair [$X_0,\;Y_0$] in Frobenius norm. Given numerical examples show that the algorithm is efficient.

• Journal of the Korean Mathematical Society
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• v.61 no.3
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• pp.427-444
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• 2024

The matrix completion problem is to predict missing entries of a data matrix using the low-rank approximation of the observed entries. Typical approaches to matrix completion problem often rely on thresholding the singular values of the data matrix. However, these approaches have some limitations. In particular, a discontinuity is present near the thresholding value, and the thresholding value must be manually selected. To overcome these difficulties, we propose a shrinkage and thresholding function that smoothly thresholds the singular values to obtain more accurate and robust estimation of the data matrix. Furthermore, the proposed function is differentiable so that the thresholding values can be adaptively calculated during the iterations using Stein unbiased risk estimate. The experimental results demonstrate that the proposed algorithm yields a more accurate estimation with a faster execution than other matrix completion algorithms in image inpainting problems.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.95-106
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• 2016

In this paper, according to the classical LSQR algorithm forsolving least squares (LS) problem, an iterative method is proposed for finding the minimum-norm pure imaginary solution of the quaternionic least squares (QLS) problem. By means of real representation of quaternion matrix, the QLS's correspongding vector algorithm is rewrited back to the matrix-form algorthm without Kronecker product and long vectors. Finally, numerical examples are reported that show the favorable numerical properties of the method.

• Journal of the Korea Society for Simulation
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• v.11 no.4
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• pp.57-68
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• 2002

The analysis of the cyclic scheduling problem in FMS using the transitive matrix has been proposed. Since the transitive matrix may explain all the relations between the places and transitions, we propose an algorithm to get good solution after slicing off some subnets from the original net based on machines operations. For analyzing the schedule problem, we considered two time functions such as produce time and waiting time using the P-invariant. In addition, we are shown the effectiveness of proposed algorithm after comparing with unfolding algorithms.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1011-1020
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• 2008

The problem of finding Cramer rule for solutions of some restricted linear equation Ax = b has been widely discussed. Recently Wang and Qiao consider the following more general problem AXB = D, $R(X){\subset}T$, $N(X){\supset}\tilde{S}$. They present the solution of above general restricted matrix equation by using generalized inverses and give an explicit expression for the elements of the solution matrix for the matrix equation. In this paper we re-consider the restricted matrix equation and give an equivalent matrix equation to it. Through the equivalent matrix equation, we derive condensed Cramer rule for above restricted matrix equation. As an application, condensed determinantal expressions for $A_{T,S}^{(2)}$ A and $AA_{T,S}^{(2)}$ are established. Based on above results, we present a method for computing the solution of a kind of restricted matrix equation.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.657-670
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• 2019

In this paper, we consider the preconditioned iterative methods for solving linear complementarity problem associated with an M-matrix. Based on the generalized Gunawardena's preconditioner, two preconditioned SSOR methods for solving the linear complementarity problem are proposed. The convergence of the proposed methods are analyzed, and the comparison results are derived. The comparison results showed that preconditioned SSOR methods accelerate the convergent rate of the original SSOR method. Numerical examples are used to illustrate the theoretical results.