• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.169-180
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• 2006

We study convergence of multisplitting method associated with a block diagonal conformable multisplitting for solving a linear system whose coefficient matrix is a symmetric positive definite matrix which is not an H-matrix. Next, we study the validity of m-step multisplitting polynomial preconditioners which will be used in the preconditioned conjugate gradient method.

• 한국멀티미디어학회논문지
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• 제11권9호
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• pp.1302-1309
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• 2008

K-means나 퍼지 군집화와 같은 전통적인 군집화 기법들이 원형(prototype)을 기반으로 하고 볼록한 형태의 집단들에 적합한 반면, 스펙트럼 군집화(spectral clustering)는 국부적인 유사성을 기반으로 전역적인 집단을 찾아내는 기법으로 오목한 형태의 집단들에도 적용할 수 있어 커널을 기반으로 하는 SVM과 더불어 각광을 받고 있다. 하지만 SVM이 그러하듯이 스펙트럼 군집화에서도 커널의 폭은 성능에 지대한 영향을 끼치는 요인으로, 이를 결정하기 위한 다양한 방법이 시도되었지만 여전히 휴리스틱에 의존하는 실정이다. 이 논문에서는 유사도 행렬이 보다 명백한 블록 대각 형태를 가지도록 하기 위해 국부적인 커널의 폭을 거리 히스토그램을 바탕으로 적응적으로 결정하는 방법을 제시한다. 제안한 방법은 스펙트럼 군집화에 사용되는 유사도 행렬(affinity matrix)이 블록 형태의 대각 행렬을 이룰 때 이상적인 결과를 낸다는 사실에 기반하고 있으며, 이를 위해서 전통적인 유클리디안 거리와 무작위 행보 거리(random walk distance)를 함께 사용한다. 제안한 방법은 기존의 방법들에서 사용하는 유사도 행렬에 비해 명확한 블록 대각 행렬을 나타내고 있음을 실험 결과를 통해 확인할 수 있다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.988-991
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• 1996

The purpose of this thesis is to develop methods of designing robust LQR/LQG controllers for time-varying systems with real parametric uncertainties. Controller design that meet desired performance and robust specifications is one of the most important unsolved problems in control engineering. We propose a new framework to solve these problems using Linear Matrix Inequalities (LMls) which have gained much attention in recent years, for their computational tractability and usefulness in control engineering. In Robust LQR case, the formulation of LMI based problem is straightforward and we can say that the obtained solution is the global optimum because the transformed problem is convex. In Robust LQG case, the formulation is difficult because the objective function and constraint are all nonlinear, therefore these are not treatable directly by LMI. We propose a sequential solving method which consist of a block-diagonal approach and a full-block approach. Block-diagonal approach gives a conservative solution and it is used as a initial guess for a full-block approach. In full-block approach two LMIs are solved sequentially in iterative manner. Because this algorithm must be solved iteratively, the obtained solution may not be globally optimal.

• 응용통계연구
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• 제35권4호
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• pp.569-577
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• 2022

비모수적 추정량의 성능을 이론적으로 비교하기 힘들 때 흔히 모의실험을 실시한다. 다양한 실험조건에서 여러 추정량에 대해 얻어진 모의실험 결과를 회귀모형을 이용해 분석하면 보다 체계적이고 정확한 비교를 할 수 있다는 것을 Kim과 Kim (2021)에서 보였다. 이 연구는 Kim과 Kim (2021)에 대한 후속연구이자 보완연구이다. 회귀모형의 오차항에 대한 분산공분산행렬에서 이분산성만 고려하고 공분산을 선행연구에서 무시했는데, 공분산을 고려하게 되면 분산공분산행렬은 블록대각행렬이 된다. 본 연구에서 블록대각행렬인 분산공분산행렬을 추정하여 분석에 이용하는 방법을 제시하였다. 이렇게 하면 명목신뢰수준을 보장하면서 유의하게 성능 차이가 나는 추정량 짝을 더 잘 찾을 수 있다는 것도 보였다.

• 경영과학
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• 제24권1호
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• pp.91-111
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• 2007

In this paper an effective two-phase approach adopting modified p-median mathematical model is proposed for grouping machines and parts in cellular manufacturing(CM). Unlike the conventional methods allowing machines and parts to be improperly assigned to cells and families, the proposed approach seeks to find the proper block diagonal solution where all the machines and parts are properly assigned to their most associated cells and families in term of the actual machine processing and part moves. Phase 1 uses the modified p-median formulation adopting new inter-machine similarity coefficient based on the non-binary production data-based part-machine incidence matrix(PMIM) that reflects both the operation sequences and production volumes for the parts to find machine cells. Phase 2 apollos iterative reassignment procedure to minimize inter-cell part moves and maximize within-cell machine utilization by reassigning improperly assigned machines and parts to their most associated cells and families. Computational experience with the data sets available on literature shows the proposed approach yields good-quality proper block diagonal solution.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권3호
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• pp.267-282
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• 2019

This paper examines how one can build a block tridiagonal structure for k-almost normal matrices and also for k-almost conjugate normal matrices. We shall see that these representations are created by unitary similarity and unitary congruance transformations, respectively. It shall be proven that the orders of diagonal blocks are 1, k + 2, 2k + 3, ${\ldots}$, in both cases. Then these block tridiagonal structures shall be reviewed for the cases where the mentioned matrices satisfy in a second-degree polynomial. Finally, for these processes, algorithms are presented.

• 대한수학회보
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• 제41권2호
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• pp.199-211
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• 2004

For positive integers $\kappa$ and p$\geq$3, let(equation omitted) where $J_{p}$ is the p${\times}$p matrix whose entries are all 1. Then, we determine the minimum permanents and minimizing matrices over (1) the face of $\Omega$(D) and (2) the face of $\Omega$($D^{*}$), where (equation omitted).

• 정보처리학회논문지A
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• 제8A권3호
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• pp.227-234
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• 2001

In this paper we propose a block-type parallel preconditioner for solving large sparse nonsymmetric linear systems, which we expect to be scalable. It is Multi-Color Block SOR preconditioner, combined with direct sparse matrix solver. For the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with Multi-Color ordering. Since most of the time is spent on the diagonal inversion, which is done on each processor, we expect it to be a good scalable preconditioner. We compared it with four other preconditioners, which are ILU(0)-wavefront ordering, ILU(0)-Multi-Color ordering, SPAI(SParse Approximate Inverse), and SSOR preconditiner. Experiments were conducted for the Finite Difference discretizations of two problems with various meshsizes varying up to $1025{\times}1024$. CRAY-T3E with 128 nodes was used. MPI library was used for interprocess communications, The results show that Multi-Color Block SOR is scalabl and gives the best performances.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권1호
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• pp.85-100
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• 2001

In this paper we propose a block-type parallel preconditioner for solving large sparse nonsymmetric linear systems, which we expect to be scalable. It is Multi-Color Block SOR preconditioner, combined with direct sparse matrix solver. For the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with Multi-Color ordering. Since most of the time is spent on the diagonal inversion, which is done on each processor, we expect it to be a good scalable preconditioner. Finally, due to the blocking effect, it will be effective for ill-conditioned problems. We compared it with four other preconditioners, which are ILU(0)-wavefront ordering, ILU(0)-Multi-Color ordering, SPAI(SParse Approximate Inverse), and SSOR preconditioner. Experiments were conducted for the Finite Difference discretizations of two problems with various meshsizes varying up to 1024 x 1024, and for an ill-conditioned matrix from the shell problem from the Harwell-Boeing collection. CRAY-T3E with 128 nodes was used. MPI library was used for interprocess communications. The results show that Multi-Color Block SOR and ILU(0) with Multi-Color ordering give the best performances for the finite difference matrices and for the shell problem only the Multi-Color Block SOR converges.