• 경영과학
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• 제11권3호
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• pp.1-11
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• 1994

Recent advances in linear programming solution methodology have focused on interior point methods. This powerful new class of methods achieves significant reductions in computer time for large linear programs and solves problems significantly larger than previously possible. These methods can be examined from points of Fiacco and McCormick's barrier method, Lagrangian duality, Newton's method, and others. This study presents a primal-dual log barrier algorithm of interior point methods for linear programming. The primal-dual log barrier method is currently the most efficient and successful variant of interior point methods. This paper also addresses a Cholesky factorization method of symmetric positive definite matrices arising in interior point methods. A special structure of the matrices, called supernode, is exploited to use computational techniques such as direct addressing and loop-unrolling. Two dense matrix handling techniques are also presented to handle dense columns of the original matrix A. The two techniques may minimize storage requirement for factor matrix L and a smaller number of arithmetic operations in the matrix L computation.

• Journal of the Korean Data and Information Science Society
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• 제27권3호
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• pp.815-825
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• 2016

Marginalized random effects models (MREMs) are often used to analyze longitudinal categorical data. The models permit direct estimation of marginal mean parameters and specify the serial correlation of longitudinal categorical data via the random effects. However, it is not easy to estimate the random effects covariance matrix in the MREMs because the matrix is high-dimensional and must be positive-definite. To solve these restrictions, we introduce two modeling approaches of the random effects covariance matrix: partial autocorrelation and the modified Cholesky decomposition. These proposed methods are illustrated with the real data from Korean genomic epidemiology study.

• International Journal of Precision Engineering and Manufacturing
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• 제5권3호
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• pp.77-84
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• 2004

A robust optimal control design is proposed in this study for rigid robotic systems under the unknown loads and the other uncertainties. The uncertainties are reflected in the performance index, where the uncertainties are bounded for the quadratic square of the states with a positive definite weighting matrix. An iterative algorithm is presented for the determination of the weighting matrix required for necessary robustness. Computer simulations have been done for a weight-lifting operation of a two-link manipulator and the simulation results shows that the proposed algorithm is very effective for a robust control of robotic systems.

• 대한수학회보
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• 제38권1호
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• pp.29-53
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• 2001

This note presents a an indirect adaptive control scheme for first-order continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. The singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That properties is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. A modification scheme based on the achievement of a modified diagonally dominant Sylvester matrix of the parameter estimates is also given as an alternative method. This diagonal dominance is achieved through estimates modification as a way to guarantee the controllability of the modified estimated model when a controllability measure of the ‘a priori’ estimated model fails. In both schemes, the use of a hysteresis switching function for the modification of the estimates is not required to ensure the nonsingularity of the Sylvester matrix of the estimates.

• 대한수학회보
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• 제47권1호
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• pp.89-102
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• 2010

This paper concerns the problem of global robust stability of a time-delay discontinuous system with a positive-defined connection matrix under polytopic-type uncertainty. In order to give the stability condition, we firstly address the existence of solution and equilibrium point based on the properties of M-matrix, Lyapunov-like approach and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. Second, we give the delay-independent and delay-dependent stability condition in terms of linear matrix inequalities (LMIs), and based on Lyapunov function and the properties of the convex sets. One numerical example demonstrate the validity of the proposed criteria.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2015년도 추계학술대회
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• pp.4-7
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• 2015

In this paper, we propose a matrix completion algorithm for Internet of Things (IoT) localization. The proposed algorithm recovers the Gram matrix of sensors by performing optimization over the Riemannian manifold of fixed-rank positive semidefinite matrices. We compute and show the closed forms of all the differentially geometric components required for applying nonlinear conjugate gradients combined with Armijo line search method. The numerical experiments show that the performance of the proposed algorithm in solving IoT localization is outstanding compared with the state-of-the-art matrix completion algorithms both in noise and noiseless scenarios.

• East Asian mathematical journal
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• 제32권1호
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• pp.13-25
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• 2016

We consider the nonlinear matrix equation $X^p+AX^qB+CXD+E=0$, where p and q are positive integers, A, B and E are $n{\times}n$ nonnegative matrices, C and D are arbitrary $n{\times}n$ real matrices. A sufficient condition for the existence of the elementwise minimal nonnegative solution is derived. The monotone convergence of Newton's method for solving the equation is considered. Several numerical examples to show the efficiency of the proposed Newton's method are presented.

• 대한수학회보
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• 제46권1호
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• pp.117-123
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• 2009

This paper is a study of some properties of a collection of bounded linear operators resulting from terraced matrices M acting through multiplication on ${\ell}^2$; the term terraced matrix refers to a lower triangular infinite matrix with constant row segments. Sufficient conditions are found for M to be posinormal, meaning that $MM^*=M^*PM$ for some positive operator P on ${\ell}^2$; these conditions lead to new sufficient conditions for the hyponormality of M. Sufficient conditions are also found for the adjoint $M^*$ to be posinormal, and it is observed that, unless M is essentially trivial, $M^*$ cannot be hyponormal. A few examples are considered that exhibit special behavior.

• 수면정신생리
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• 제8권1호
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• pp.67-71
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• 2001

Independent Component Analysis (ICA) is a blind source separation method using unsupervised learning and mutual information theory created in the late eighties and developed in the nineties. It has already succeeded in separating eye movement artifacts from human scalp EEG recording. Several characteristic sleep waves such as sleep spindle, K-complex, and positive occipital sharp transient of sleep (POSTS) can be recorded during sleep EEG recording. They are used as stage determining factors of sleep staging and might be reflections of unknown neural sources during sleep. We applied the ICA method to sleep EEG for sleep waves separation. Eighteen channel scalp longitudinal bipolar montage was used for the EEG recording. With the sampling rate of 256Hz, digital EEG data were converted into 18 by n matrix which was used as a original data matrix X. Independent source matrix U (18 by n) was obtained by independent component analysis method ($U=W{\timex}X$, where W is an 18 by 18 matrix obtained by ICA procedures). ICA was applied to the original EEG containing sleep spindle, K-complex, and POSTS. Among the 18 independent components, those containing characteristic shape of sleep waves could be identified. Each independent component was reconstructed into original montage by the product of inverse matrix of W (inv(W)) and U. The reconstructed EEG might be a separation of sleep waves without other components of original EEG matrix X. This result (might) demonstrates that characteristic sleep waves may be separated from original EEG of unknown mixed neural origins by the Independent Component Analysis (ICA) method.

• 응용통계연구
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• 제28권2호
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• pp.211-219
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• 2015

일반화 선형혼합모델은 일반적으로 경시적 범주형 자료를 분석하는데 사용된다. 이 모델에서 임의효과는 반복 측정치들의 시간에 따른 의존성을 설명한다. 임의효과 공분산행렬의 추정은 여러가지 제약조건들 때문에 쉽지 않은 문제이다. 제약조건으로는 행렬의 모수들의 수가 많으며, 또한 추정된 공분산행렬은 양정치성을 만족하여야 한다. 이러한 제한을 극복하기 위해, 임의효과 공분산행렬의 모형화를 위한 여러가지 방법이 제안되었다: 수정 단냠레스키분해, 이동평균 단냠레스키분해와 부분 자기상관행렬을 이용한 방법이 있다. 이 논문에서 위의 제안된 방법들을 소개한다.