• Journal of the Korean Society of Manufacturing Process Engineers
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• v.8 no.3
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• pp.21-26
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• 2009

The finite element analysis of metal forming processes often fails because of severe mesh distortion at large deformation. As the concept of meshless methods, only nodal point data are used for modeling and solving. As the main feature of these methods, the domain of the problem is represented by a set of nodes, and a finite element mesh is unnecessary. This computational methods reduces time-consuming model generation and refinement effort. It provides a higher rate of convergence than the conventional finite element methods. The displacement shape functions are constructed by the reproducing kernel approximation that satisfies consistency conditions. In this research, A meshless method approach based on the reproducing kernel particle method (RKPM) is applied with metal forming analysis. Numerical examples are analyzed to verify the performance of meshless method for metal forming analysis.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.599-603
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• 2002

We propose a new meshfree method to be called the fast moving least square reproducing kernel collocation method(FCM). This methodology is composed of the fast moving least square reproducing kernel(FMLSRK) approximation and the point collocation scheme. Using point collocation makes the meshfree method really come true. In this paper, FCM Is shown to be a good method at least to calculate the numerical solutions governed by second order elliptic partial differential equations with geometric singularity or geometric multi-scales. To treat such problems, we use the concept of variable dilation parameter.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1452-1455
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• 1997

This paper studies the problem of approximating commensurate input delay sustems by finite dimensional systems based on the Hankel singular values. I is shown that the Gankel singular values are solutions a trancendental equation and the Hankel singular vectors are obtained form the kernel of the matrix. The computaioin is carried out in state spae framework. Once singular values and vectors are calcualted, finite dimensional approximated systems are constructed using stadnard linear system computational tools. An example is included.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.631-644
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• 2008

In this paper, we present a new method for solving a nonlinear two-point boundary value problem with finitely many singularities. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximation $u_n(x)$ to the exact solution u(x) is obtained and is proved to converge to the exact solution. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other.

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.507-516
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• 2007

Multinomial logistic regression is probably the most popular representative of probabilistic discriminative classifiers for multiclass classification problems. In this paper, a kernel variant of multinomial logistic regression is proposed by combining a Newton's method with a bound optimization approach. This formulation allows us to apply highly efficient approximation methods that effectively overcomes conceptual and numerical problems of standard multiclass kernel classifiers. We also provide the approximate cross validation (ACV) method for choosing the hyperparameters which affect the performance of the proposed approach. Experimental results are then presented to indicate the performance of the proposed procedure.

• Interaction and multiscale mechanics
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• v.2 no.2
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• pp.129-151
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• 2009

This paper presents a meshfree procedure using a convex generalized meshfree (GMF) approximation for the large deformation analysis of particle-reinforced rubber compounds on microscopic level. The convex GMF approximation possesses the weak-Kronecker-delta property that guarantees the continuity of displacement across the material interface in the rubber compounds. The convex approximation also ensures the positive mass in the discrete system and is less sensitive to the meshfree nodal support size and integration order effects. In this study, the convex approximation is generated in the GMF method by choosing the positive and monotonic increasing basis function. In order to impose the periodic boundary condition in the unit cell method for the microscopic analysis, a singular kernel is introduced on the periodic boundary nodes in the construction of GMF approximation. The periodic boundary condition is solved by the transformation method in both explicit and implicit analyses. To simulate the interface de-bonding phenomena in the rubber compound, the cohesive interface element method is employed in corporation with meshfree method in this study. Several numerical examples are presented to demonstrate the effectiveness of the proposed numerical procedure in the large deformation analysis.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.299-304
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• 1996

This paper studies the rational approximation of multiple input delay systems using the Hankel singular values and vectors, which are the soultion of a transcendental equation. Rational approximatants are obtained from output normal realizations which are constructed by the Hankel singular values and vectors. Consequently, it is shown that rational approximants by output normal realization preserve intrinsic properties of time delay systems than Pade approximants.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.467-475
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• 1994

In 1983 Harmand and Lima [5] proved that if X is a Banach space for which K(X), the space of compact linear operators on X, is an M-ideal in L(X), the space of bounded linear operators on X, then it has the metric compact approximation property. A strong converse of the above result holds if X is a closed subspace of either $\elll_p(1 < p < \infty) or c_0 [2,15]$. In 1979 J. Johnson [7] actually proved that if X is a Banach space with the metric compact approximation property, then the annihilator K(X)^\bot$ of K(X) in $L(X)^*$ is the kernel of a norm-one projection in $L(X)^*$, which is the case if K(X) is an M-ideal in L(X).

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.3
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• pp.308-314
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• 1998

This paper studies the problem of computing the Hankel singular values and vectors in the input delay systems. It is shown that the Hankel singular values are solutions to a transcendental equation and the Hankel singular vectors are obtained from the kernel of the matrix. The computation is carried out in state space framework. Finally, Hankel approximation of a simple example shows the usefulness of this study.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.1
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• pp.194-204
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• 1997

In this paper, we consider the rational approximation of multiple input delay systems. The method of computing Hankel singular values and vectors is firstly introduced, where explicitly shows the structure of the corresponding Hankel singular vectors. Secondly, rational approximants are obtained from output nor- mal relizations, which are constructed by Hankel singular values and vectors. As a result, it is shown that rational approximants by output normal realization preserve intrinsic properties of time delay systems than Pad'e approximants.