• Korean Management Science Review
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• v.14 no.2
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• pp.69-79
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• 1997

The computational speed of interior point method of linear programming depends on the speed of Cholesky factorization. If the coefficient matrix A has dense columns then the matrix A.THETA. $A^{T}$ becomes a dense matrix. This causes Cholesky factorization to be slow. We study an efficient implementation method of the dense column splitting among dense column resolving technique and analyze the relation between dense column splitting and order methods to improve the sparsity of Cholesky factoror.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.727-741
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• 2010

In this paper, we study the convergence of relaxed two-stage multisplitting method using H-compatible splittings or SOR multisplitting as inner splittings and an outer splitting for solving a linear system whose coefficient matrix is an H-matrix. We also provide numerical experiments for the convergence of the relaxed two-stage multisplitting method.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.489-500
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• 2009

In this paper, we study the convergence of relaxed two-stage multisplitting method using M-splittings or SOR multi splitting as inner splittings and an outer splitting for solving a linear system whose coefficient matrix is an M-matrix. We also provide numerical experiments for the convergence of the relaxed two-stage multisplitting method.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1067-1074
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• 2011

In this paper, a preconditioned mixed-type splitting iterative method for solving the linear systems Ax = b is presented, where A is a Z-matrix. Then we also obtain some results to show that the rate of convergence of our method is faster than that of the preconditioned AOR (PAOR) iterative method and preconditioned SOR (PSOR) iterative method. Finally, we give one numerical example to illustrate our results.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.773-785
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• 1999

Shifts of finite type are represented by nonnegative integral square matrics, and conjugacy between two shifts of finite type is determined by strong shift equivalence between the representing nonnegative intergral square matrices. But determining strong shift equivalence is usually a very difficult problem. we develop splittings and amalgamations of nonnegative integral matrices, which are analogues of those of directed graphs, and show that two nonnegative integral square matrices are strong shift equivalent if and only if one is obtained from a higher matrix of the other matrix by a series of amalgamations.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.709-714
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• 2000

A splitting method for the direct numerical simulation of solid-liquid mixtures is presented, where a symmetric pressure equation is newly proposed. Through numerical experiment, it is found that the newly proposed splitting method works well with a matrix-free formulation fer some bench mark problems avoiding an erroneous pressure field which appears when using the conventional pressure equation of a splitting method. When deriving a typical pressure equation of a splitting method, the motion of a solid particle has to be approximated by the 'intermediate velocity' instead of treating it as unknowns since it is necessary as a boundary condition. Therefore, the motion of a solid particle is treated in such an explicit way that a particle moves by the known form drag (pressure drag) that is calculated from the pressure equation in the previous step. From the numerical experiment, it was shown that this method gives an erroneous pressure field even for the very small time step size as a particle velocity increases. In this paper, coupling the unknowns of particle velocities in the pressure equation is proposed, where the resulting matrix is reduced to the symmetric one by applying the projector of the combined formulation. It has been tested over some bench mark problems and gives reasonable pressure fields.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.28 no.1
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• pp.69-78
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• 2014

In this paper, characteristics of wireless power transfer (WPT) systems using magnetically coupled resonance scheme with relay coils are investigated and modeled. Especially, asymmetric frequency splitting characteristics in over-coupled region of WPT with relays are measured and accurately modeled. Transmitter, receiver, and relay coils are modeled with R, L, C equivalent circuits. Using these circuit models and mutual inductances between coils, a WPT system is described with a linear matrix equation. For under-coupled region, a matrix is simplified considering only mutual inductances between adjacent coils. An analytical transfer characteristic of WPT system vs. distance is extracted using an inverse matrix that is acquired by Gauss elimination method for the simplified matrix. For over-coupled region, a matrix considering mutual inductances between non-adjacent coils is used to predict a frequency splitting characteristics accurately. A 6.3MHz WPT system with relay coils is implemented and measured. An accuracy of the model is investigated by comparing the output of the model with the measured results.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.489-506
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• 2020

The spatial fractional diffusion equation can be discretized by employing the implicit finite difference scheme using the shifted Grünwald formula. The discretized linear system is obtained, whose the coefficient matrix has a diagonal-plus-Toeplitz structure. In order to solve the diagonal-plus-Toeplitz linear system, on the basis of circulant and skew-circulant splitting (CSCS splitting), we construct a new and efficient iterative method, called DSCS iterative methods, which have two parameters. Than we prove the convergence of DSCS methods. As a focus, we derive the simple and effective values of two optimal parameters under some restrictions. Some numerical experiments are carried out to illustrate the validity and accuracy of the new methods.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.571-584
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• 1998

We look for methods and conditions to make use of cyclicity in come matrix problems not only for parallel computa-tion but also to reduce the problem size and accelerate convergence. It has been shown that some form of reducibility not necessarily cyclicity is enough for such purposes.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.1495-1498
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• 2003

Recently, self-healing methods of a cracked matrix, especially polymeric composite materials, became the center of engineering researchers. In this paper, we summarized the self-healing concept for polymeric composite materials and investigated the effect of microparticle on the crack growth behavior in colorless and transparent matrix by experimental observation to describe the crack propagation around the microparticle inside epoxy matrix composite. Compression splitting test for the specimen involving microparticle was conducted. In addition, FE analysis was pursued to present the stress contour around microparticle in the matrix. Through the experiments and FE analysis, we found that the size. relative position, bonding condition and relative stiffness of microparticle are important parameters to decide the direction of crack propagation, which is related to the rupture of microparticle for self-healing