• Journal of KIISE:Software and Applications
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• v.31 no.5
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• pp.577-585
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• 2004

Storing and estimating the high order probability distribution of classifiers and class labels is exponentially complex and unmanageable without an assumption or an approximation, so we rely on an approximation scheme using the dependency. In this paper, as an extended study of the second-order dependency-based approximation, the probability distribution is optimally approximated by the third-order dependency. The proposed third-order dependency-based approximation is applied to the combination of multiple classifiers recognizing handwritten numerals from Concordia University and the University of California, Irvine and its usefulness is demonstrated through the experiments.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2483-2491
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• 2002

This study presents an efficient method for robust optimal design. In order to avoid the excessive evaluations of the exact performance functions, two-point diagonal quadratic approximation method is employed for approximating them during optimization process. This approximation method is one of the two point approximation methods. Therefore, the second order sensitivity information of the approximated performance functions are calculated by an analytical method. As a result, this enables one to avoid the expensive evaluations of the exact $2^{nd}$ derivatives of the performance functions unlike the conventional robust optimal design methods based on the gradient information. Finally, in order to show the numerical performance of the proposed method, one mathematical problem and two mechanical design problems are solved and their results are compared with those of the conventional methods.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.3040-3052
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• 2000

For effective construction of second-order response surface models, an efficient quad ratic approximation method is proposed in the context of trust region model management strategy. In the proposed method, although only the linear and quadratic terms are uniquely determined using 2n+1 design points, the two-factor interaction terms are mathematically updated by normalized quasi-Newton formula. In order to show the numerical performance of the proposed approximation method, a sequential approximate optimizer is developed and solves a typical unconstrained optimization problem having 2, 6, 10, 15, 30 and 50 design variables, a gear reducer system design problem and two dynamic response optimization problems with multiple objectives, five objectives for one and two objectives for the other. Finally, their optimization results are compared with those of the CCD or the 50% over-determined D-optimal design combined with the same trust region sequential approximate optimizer. These comparisons show that the proposed method gives more efficient than others.

• Korean Management Science Review
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• v.15 no.2
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• pp.125-142
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• 1998

The aggregation on linear large-scale dynamic systems is examined in this paper and a "two-step" approach is proposed. In this procedure, the aggregated system consists of two subsystems. The first subsystem represents aggregation through the retainment of dominant eigenvalues of the original system, leading to a first approximation of the desired output of the original system. The purpose of augmenting it with a second subsystem is to provide an estimation of the error on the first approximation, thus permitting a second correction to the output approximation and resulting in an output approximation of greater accuracy. Optimization techniques are discussed for the determination of unknown parameters in the aggregated system. These techniques use minimization principles of certain suitable performance indices and are developed for both single input-single output and multiple input-multiple output system. Numerical examples illustrating these procedures are given and the results are compared with those obtained using existing methods. Finally, a pharmacokinetics problem is studied from the aggregation point of view.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.927-945
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• 2012

An approximation of singular source terms in elliptic problems is developed and analyzed. Under certain assumptions on the curve where the singular source is defined, the second order convergence in the maximum norm can be proved. Numerical results present its better performance compared to previously developed regularization techniques.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.23-40
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• 1998

Mixed finite element method is developed to approxi-mate the solution of the initial-boundary value problem for a strongly nonlinear second-order hyperbolic equation in divergence form. Exis-tence and uniqueness of the approximation are proved and optimal-order $L\infty$-in-time $L^2$-in-space a priori error estimates are derived for both the scalar and vector functions approximated by the method.

• Journal of computational fluids engineering
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• v.11 no.1 s.32
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• pp.8-15
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• 2006

The existing approximations of diffusion flux in unstructured cell-centered finite volume methods are examined in detail with each other and clarified to have indefinite expressions in several respects. A new numerical approximation of diffusion flux at cell face center is then proposed, which is second-order accurate even on irregular grids and may be easily implemented in CFD code using cell-centered finite volume method with unstructured grids composed of arbitrary convex polyhedral shape.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.6
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• pp.477-482
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• 2016

This paper presents a simple approximation-based design approach for consensus tracking of heterogeneous second-order nonlinear systems under a directed network. All nonlinearities of followers are assumed to be unknown and non-identical. In the controller design procedure, graph-independent error surfaces are used and an unimplementable intermediate controller for each follower is designed at the first design step. Then, by adding and subtracting a graph-based term at the second step, the actual controller for each follower is designed by using one neural network employed to estimate a lumped and distributed nonlinearity. Therefore, the proposed local controller for each follower has a simpler structure than existing approximation-based consensus tracking controllers for multi-agent systems with unmatched nonlinearities.

• Korean Journal of Mathematics
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• v.26 no.3
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• pp.467-481
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• 2018

In this paper we present a postprocessing scheme for the Raviart-Thomas mixed finite element approximation of the second order elliptic eigenvalue problem. This scheme is carried out by solving a primal source problem on a higher order space, and thereby can improve the convergence rate of the eigenfunction and eigenvalue approximations. It is also used to compute a posteriori error estimates which are asymptotically exact for the $L^2$ errors of the eigenfunctions. Some numerical results are provided to confirm the theoretical results.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.6
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• pp.331-337
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• 2018

This paper presents dynamic algorithm of the MLS(moving least squares) difference method using first order differential Approximation. The governing equations are only discretized by the first order MLS derivative approximation. The system equation consists of an assembly of the approximate function, so the shape of system equation is similar to FEM(finite element method). The CDM(central difference method) is used for time integration of dynamic equilibrium equation. The natural frequency analyses of the MLS difference method and FEM are performed, and two analysis results are compared. Also, the accuracy of the proposed numerical method is verified by displaying the dynamic analysis results together with the results by the existing second order differential approximation. In the process of assembling the first order MLS derivative approximation, the oscillation error was suppressed and the stress distribution was interpreted as relatively uniform.