• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.687-696
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• 2010

In this paper, an algorithm for computing the sparse approximate inverse factor of matrix $A^{T}\;A$, where A is an $m\;{\times}\;n$ matrix with $m\;{\geq}\;n$ and rank(A) = n, is proposed. The computation of the inverse factor are done without computing the matrix $A^{T}\;A$. The computed sparse approximate inverse factor is applied as a preconditioner for solving normal equations in conjunction with the CGNR algorithm. Some numerical experiments on test matrices are presented to show the efficiency of the method. A comparison with some available methods is also included.

• Journal of Ship and Ocean Technology
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• v.7 no.3
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• pp.56-65
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• 2003

The hull monitoring systems of container ships with four long-base gages give enough information for identifying the hull girder loads such as bending and torsional moments. But such a load-identification for container ships has not been known. In this paper, a load-identification method is suggested in terms of a linear matrix equation that the measured strain vector equals to the multiplication of the transformation matrix and the desired strain component vector. The equation is proved to be mathematically complete by the property of positive-definite determinant of the transformation matrix. The method is applied to a hull stress monitoring system for 8100TED container ship during sea trial, and the estimated external loads illustrate reasonable results in comparison with the pre-estimated results. This moment decomposition concept has also been tested in real operation conditions. The typical phenomena over the Suez Canal illustrated very suitable results comparing with the physical understandings. Henceforth, one can effectively use the proposed concept to monitor the hull girder loads such as bending and torsional moments.

• Journal of Korean Institute of Industrial Engineers
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• v.25 no.3
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• pp.290-297
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• 1999

In interior point methods for linear programming, we must solve a linear system with a symmetric positive definite matrix at every iteration, and Cholesky factorization is generally used to solve it. Therefore, if Cholesky factorization is not done successfully, many iterations are needed to find the optimal solution or we can not find it. We studied methods for improving the numerical stability of Cholesky factorization and the accuracy of the solution of the linear system.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.627-647
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• 2015

In this paper, we construct the Schr$\ddot{o}$dinger-Weil representation of the Jacobi group associated with a positive definite symmetric real matrix of degree m and find covariant maps for the Schr$\ddot{o}$dinger-Weil representation.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.35-38
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• 1995

Let A be a symmetric positive definite Cartan matrix. As in [4], we denote by U the quantum group arising from A and $U_\lambda$ be the corresponding quantum group at a root of unity $\lambda$. In [4], Lusztig constructed irreducible highest weight $U_\lambda$-modules $L_\lambda(z)$ for $z \in Z^n$ and showed that $L_\lambda(z)$ is of finite dimension over C if and only if $z \in (Z^+)^n$.

• Proceedings of the KIEE Conference
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• 2001.11c
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• pp.76-79
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• 2001

This paper is concerned with a stability analysis of Madam Type fuzzy systems. It Introduces the canonical form of an unforced fuzzy system and its stability theorem suggested in the previous study. Then it gives new simplified stability conditions based on the Lyapunov function method. A common positive definite matrix in the stability conditions is searched by the LMI method.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.125-133
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• 2002

Recently, Several inequalities Khatri-Rao Products of two four partitioned blocks positive definite real symmetry matrices are established by Liu in[Lin. Alg. Appl. 289(1999): 267-277]. We extend these results in two ways. First, the results are extended to two any partitioned blocks Hermitian matrices. Second, necessary and sufficient conditions under which these inequalities become equalities are presented.

• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.103-117
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• 2017

In longitudinal data analysis, the serial correlation of repeated outcomes must be taken into account using covariance matrix. Modeling of the covariance matrix is important to estimate the effect of covariates properly. However, It is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcome the restrictions, several Cholesky decomposition approaches for the covariance matrix were proposed: modified autoregressive (AR), moving average (MA), ARMA Cholesky decompositions. In this paper we review them and compare the performance of the approaches using simulation studies.

• Journal of Institute of Control, Robotics and Systems
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• v.3 no.2
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• pp.109-114
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• 1997

In this paper, we present an output feedback $H^\infty$controller design method and derive the sufficient condition of the bounded real lemma for linear systems with multiple delays in states. For state delayed systems, sufficient conditions for the existence $\kappa$-th order $H^\infty$controllers are given in terms of three linear matrix inequalities(LMIs). Furthermore, we show how to construct such controllers from the positive definite solutions of their LMIs and given an example to illustrate the validitiy of the proosed design procedure.

• Transactions on Control, Automation and Systems Engineering
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• v.1 no.2
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• pp.106-112
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• 1999

This paper presents an H$\infty$ controller design method for linear systems with time-varying delayed states, inputs, and measurement outputs. Using a Lyapounov unctional , the stability for delay systems is discussed independently of time delays . And a sufficient condition for the existence of H$\infty$ controllers of n-th order is given in terms of three matrix inequalities. Based on the positive-definite solutions of their matrix inequalities, we briefly explain how to construct H$\infty$ construct H$\infty$ controller, which stabilizes time-delay systems independently of delays and guarantees an H$\infty$ norm bound.