• Korean Journal of Computational Design and Engineering
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• v.11 no.1
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• pp.1-10
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• 2006

This paper addresses B-spline curve approximation of a set of ordered points to a specified toterance. The important issue in this problem is to reduce the number of control points while keeping the desired accuracy in the resulting B-spline curve. In this paper we propose a new method for error-bounded B-spline curve approximation based on adaptive selection of dominant points. The method first selects from the given points initial dominant points that govern the overall shape of the point set. It then computes a knot vector using the dominant points and performs B-spline curve fitting to all the given points. If the fitted B-spline curve cannot approximate the points within the tolerance, the method selects more points as dominant points and repeats the curve fitting process. The knots are determined in each step by averaging the parameters of the dominant points. The resulting curve is a piecewise B-spline curve of order (degree+1) p with $C^{(p-2)}$ continuity at each knot. The shape index of a point set is introduced to facilitate the dominant point selection during the iterative curve fitting process. Compared with previous methods for error-bounded B-spline curve approximation, the proposed method requires much less control points to approximate the given point set with the desired shape fidelity. Some experimental results demonstrate its usefulness and quality.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.949-961
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• 1995

Let f be a smooth G map from a nonsingular real algebraic G variety to an equivariant Grassmann variety. We use some G vector bundle theory to find a necessary and sufficient condition to approximate f by an entire rational G map. As an application we algebraically approximate a smooth G map between G spheres when G is an abelian group.

• Speech Sciences
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• v.11 no.2
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• pp.211-216
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• 2004

In this paper, we present a fast encoding algorithm for vector quantization with an approximate Euclidean distance calculation. An approximation is performed by converting floating point to the near integer. An inequality between the approximate Euclidean distance and the nearest distance is developed to avoid unnecessary distance calculations. Since the proposed algorithm rejects those codewords that are impossible to be the nearest codeword, it produces the same output as conventional full search algorithm.

• Journal of Magnetics
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• v.6 no.2
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• pp.43-46
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• 2001

The reflection-amplitude approximation is used to calculate the interlayer exchange coupling in (001) Co/Cu/Co multilayers. The dependence of the phase factor of the reflection amplitude on the energy and wave vector is included. The contribution of each period is calculated and the results are compared with those from asymptotic behavior. It is shown that the energy and wave-vector dependence of the phase factor may affect the interlayer exchange coupling significantly.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.383-393
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• 2021

In this paper, numerical techniques are presented for solving initial value problems of fractional differential equations with variable coefficients. The method is derived by applying a Taylor vector approximation. Moreover, the operational matrix of fractional integration of a Taylor vector is provided in order to transform the continuous equations into a system of algebraic equations. Furthermore, numerical examples demonstrate that this method is applicable and accurate.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.27 no.1
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• pp.51-56
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• 2017

This paper presents an approach of predicting the radiated noise due to the structural vibration by internal harmonic forces using the doubly asymptotic approximation (DAA). Acoustic transfer vector is derived from the Helmholtz integral equation and the fluid-structure interaction relation of DAA. Numerical results and analytical results of radiated noise for a cylindrical shell were compared and showed that they were consistent in most of frequencies and radiation directions, but showed errors in some radiated directions in the mid-frequency region. Despite these errors, the prediction method will be suitable for practical radiated noise prediction.

• Journal of Korean Institute of Industrial Engineers
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• v.38 no.1
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• pp.1-6
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• 2012

We consider a two-dimensional vector packing problem in which each item has size in x- and y-coordinates. The purpose of this paper is to provide a ground work on how hard two-dimensional vector packing problems are for large items. We prove that the problem with each item greater than 1/2-${\varepsilon}$ either in x- or y-coordinates for 0 < ${\varepsilon}$ ${\leq}$ 1/6 has no APTAS unless P = NP.

• Management Science and Financial Engineering
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• v.16 no.1
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• pp.81-117
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• 2010

Semi-supervised learning incorporates unlabeled examples, whose labels are unknown, as well as labeled examples into learning process. Although transductive support vector machine (TSVM), one of semi-supervised learning models, was proposed about a decade ago, its application to large-scaled data has still been limited due to its high computational complexity. Our previous research addressed this limitation by introducing a branch-and-bound algorithm for finding an optimal solution to TSVM. In this paper, we propose three new techniques to enhance the performance of the branch-and-bound algorithm. The first one tightens min-cut bound, one of two bounding strategies. Another technique exploits a graph-based approximation to a support vector machine problem to avoid the most time-consuming step. The last one tries to fix the labels of unlabeled examples whose labels can be obviously predicted based on labeled examples. Experimental results are presented which demonstrate that the proposed techniques can reduce drastically the number of subproblems and eventually computational time.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.39 no.3
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• pp.44-52
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• 2002

In this paper, we present an analytical method for decision boundary feature extraction for neural networks. It has been shown that all the features necessary to achieve the same classification accuracy xxxas in the original space can be obtained from the vectors normal to decision boundaries. However, the vector normal to the decision boundary of a neural network has been calculated numerically using a gradient approximation. This process is time-consuming and the normal vector may be inaccurately estimated. In this paper, we propose a method to improve the performance of the previous decision boundary feature extraction for neural networks by accurately calculating the normal vector When the normal vectors are computed analytically, it is possible to reduce the processing time significantly and improve the performance of the previous implementation that employs numerical approximation.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.137-144
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• 1995

Hierarchical Bayes estimations of exchangeable mean vector of a multivariate Poisson distribution are obtained. Since sophiscated analytic integration procedures are needed, the Laplace method is employed in order tocompute these estimations approximately. An example is presented.