• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.495-509
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• 2002

We propose variants of the modified incomplete Cho1esky factorization preconditioner for a symmetric positive definite (SPD) matrix. Spectral properties of these preconditioners are discussed, and then numerical results of the preconditioned CG (PCG) method using these preconditioners are provided to see the effectiveness of the preconditioners.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1950-1963
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• 1995

A modification of the approximate-factorization method is made to accelerate the convergency rate and to take sufficiently large Courant number without loss of accuracy. And a stable implicit finite-difference scheme for solving the incompressible Navier-Stokes equations employed above modified method is developed. In the present implicit scheme, the volume fluxes with contravariant velocity components and the pressure formulation in curvilinear coordinates is adopted. In order to satisfy the continuity condition completely and to remove spurious errors for the pressure, the Navier-Stokes equations are solved by a modified SMAC scheme using a staggered gird. The upstream-difference scheme such as the QUICK scheme is also employed to the right hand side. The implicit scheme is unconditionally stable and satisfies a diagonally dominant condition for scalar diagonal linear systems of implicit operator on the left hand side. Numerical results for some test calculations of the two-dimensional flow in a square cavity and over a backward-facing step are obtained using both usual approximate-factorization method and the modified one, and compared with each other. It is shown that the present scheme allows a sufficiently large Courant number of O(10$^{2}$) and reduces the computing time.

• Journal of the Korean Physical Society
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• v.73 no.9
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• pp.1211-1218
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• 2018

Within the framework of the modified factorization method, we solve the $Schr{\ddot{o}}dinger$ equation with the modified Yukawa potential. The energy spectrum is obtained using the Pekeris approximation scheme for the centrifugal term. The thermodynamic properties, including the vibrational partition function, vibrational mean energy, vibrational mean free energy, vibrational specific heat capacity and vibrational entropy, are calculated. As a special case, we compare our result with that work of Dong [Int. J. Quant. Chem. 107, 366 (2007)] and find good agreement.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.9
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• pp.4684-4705
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• 2019

Collaborative filtering recommender systems are vulnerable to shilling attacks in which malicious users may inject biased profiles to promote or demote a particular item being recommended. To tackle this problem, many robust collaborative recommendation methods have been presented. Unfortunately, the robustness of most methods is improved at the expense of prediction accuracy. In this paper, we construct a robust Bayesian probabilistic matrix factorization model for collaborative filtering recommender systems by incorporating the detection of user anomaly rating behaviors. We first detect the anomaly rating behaviors of users by the modified K-means algorithm and target item identification method to generate an indicator matrix of attack users. Then we incorporate the indicator matrix of attack users to construct a robust Bayesian probabilistic matrix factorization model and based on which a robust collaborative recommendation algorithm is devised. The experimental results on the MovieLens and Netflix datasets show that our model can significantly improve the robustness and recommendation accuracy compared with three baseline methods.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.2
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• pp.108-120
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• 1992

An ADI model for linearized shallow water equation is modified using the method of factorization. In order to show its validity. the computational results are compared both with the analytical solution and with those from existing models, for a rectangualr domain with constant and varying amplitudes at the open boundary. It is shown the accuracy of numerical solutions depends on the size of time step. depth and bottom friction. The modified ADI model is shown to be superior to the existing models such as Leendertse (1971). Butler (1980) and Sheng (1983).

• The Journal of the Acoustical Society of Korea
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• v.43 no.4
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• pp.369-382
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• 2024

To suppress the reverberation in the active sonar system, the non-negative matrix factorization-based reverberation suppression methods have been researched recently. An estimation loss function, which makes the multiplication of basis matrices same as the input signals, has to be considered to design the non-negative matrix factorization methods, but the conventional method simply chooses the Kullback-Leibler divergence asthe lossfunction without any considerations. In this paper, we examined that the Kullback-Leibler divergence is the best lossfunction or there isthe other loss function enhancing the performance. First, we derived a modified reverberation suppression algorithm using the generalized beta-divergence function, which includes the Kullback-Leibler divergence. Then, we performed Monte-Carlo simulations using synthesized reverberation for the modified reverberation suppression method. The results showed that the Kullback-Leibler divergence function (β = 1) has good performances in the high signal-to-reverberation environments, but the intermediate function (β = 1.25) between Kullback-Leibler divergence and Euclidean distance has better performance in the low signal-to-reverberation environments.

• International Journal of Aeronautical and Space Sciences
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• v.12 no.4
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• pp.318-330
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• 2011

This paper investigates the convergence characteristics of the modified artificial compressibility method proposed by Turkel. In particular, a focus is mode on the convergence characteristics due to variation of the preconditioning factor (${\alpha}_u$) and the artificial compressibility (${\beta}$) in conjunction with an upwind method. For the investigations, a code using the modified artificial compressibility is developed. The code solves the axisymmetric incompressible Reynolds averaged Navier-Stokes equations. The cell-centered finite volume method is used in conjunction with Roe's approximate Riemann solver for the inviscid flux, and the central difference discretization is used for the viscous flux. Time marching is accomplished by the approximated factorization-alternate direction implicit method. In addition, Menter's k-${\omega}$ shear stress transport turbulence model is adopted for analysis of turbulent flows. Inviscid, laminar, and turbulent flows are solved to investigate the accuracy of solutions and convergence behavior in the modified artificial compressibility method. The possible reason for loss of robustness of the modified artificial compressibility method with ${\alpha}_u$ >1.0 is given.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1998.10a
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• pp.63-66
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• 1998

In the implementation of the simplex method program, the representation and the maintenance of basis matrix is very important, In the experimental study, we investigates Suhl's idea in the LU factorization and LU update of basis matrix. First, the triangularization of basis matrix is implemented and its efficiency is shown. Second, various technique in the dynamic Markowitz's ordering and threshold pivoting are presented. Third, modified Forrest-Tomlin LU update method exploiting sparsity is presented. Fourth, as a storage scheme of LU factors, Gustavson data structure is explained. Fifth, efficient timing of reinversion is developed. Finally, we show that modified Forrest-Tomlin method with Gustavson data structure is superior more than 30% to the Reid method with linked list data structure.

• 전기의세계
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• v.30 no.6
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• pp.375-385
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• 1981

New algorithms are derived for nonlinear programming problems which are characterized by their large variables and equality and inequality constraints. The algorithms are based upon the introduction of the Dependent-Variable-Elimination method, Independent-Variable-Reduction method, Optimally-Ordered-Triangular-Factorization method, Equality-Inequality-Sequential-Satisfaction method, etc. For a case study problem relating to the optimal determination of load flow in a 10-bus, 13-line sample power system, several approaches are undertaken, such as SUMT, Lagrange's Multiplier method, sequential applications of linear and quadratic programming method. For applying the linear programming method, the conventional simplex algorithm is modified to the large-system-oriented one by the introduction of the Two-Phase method and Variable-Upper-Bounding method, thus resulting in remarkable savings in memory requirements and computing time. The case study shows the validity and effectivity of the algorithms presented herein.

• Structural Engineering and Mechanics
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• v.62 no.3
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• pp.297-302
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• 2017

Structural reanalysis is frequently utilized to reduce the computational cost so that the process of design or optimization can be accelerated. The supports can be regarded as the design variables and may be modified in various types of structural optimization problems. The location, number, and type of supports can make a great impact on the performance of the structure. This paper presents a unified method for structural static reanalysis with imposition or relaxation of some support constraints. The information from the initial analysis has been fully utilized and the computational time can be significantly reduced. Numerical examples are used to validate the effectiveness of the proposed method.