• 대한수학회지
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• 제48권1호
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• pp.133-146
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• 2011

We employ a hyperbolic tangent function to construct nonlinear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations compared with those of existing non-linear transformation methods.

• 충청수학회지
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• 제22권2호
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• pp.141-148
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• 2009

We consider various algorithms calculating best onesided simultaneous approximations. We assume that X is a compact subset of $\mathbb{R}^{m}$ satisfying $X=\overline{intX}$, S is an n-dimensional subspace of C(X), and $\mu$ is any 'admissible' measure on X. For any l-tuple $f_1,\;{\cdots},\;f_{\ell}$ in C(X), we present various ideas for best approximation to F from S(F). The problem of best (both one and two-sided) approximation is a linear programming problem.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.527-545
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• 2021

The aim of this article is to give a numerical method for solving Abel's general fuzzy linear integral equations with arbitrary kernel. The method is based on approximations of fractional integrals and Caputo derivatives. The convergence analysis for the proposed method is also given and the applicability of the proposed method is illustrated by solving some numerical examples. The results show the utility and the greater potential of the fractional calculus method to solve fuzzy integral equations.

• 충청수학회지
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• 제23권3호
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• pp.435-442
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• 2010

This paper is concerned with algorithm for calculating one-sided best simultaneous approximation, in the case of continuous functions. we will apply any subgradient algorithm. In other words, we consider the algotithms from a mathematical, rather then computational, point of view.

• Journal of the Korean Data and Information Science Society
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• 제27권4호
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• pp.959-967
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• 2016

자산의 수익에 대한 분포 가정은 파생 상품의 가치 평가에 매우 중요한 역할을 한다. Elberlein과 Keller (1995)는 오랜 기간에 걸친 주식 자료를 바탕으로 혼합 자산의 분포에 대한 다양한 검정을 수행한 결과, 정규성 가정이 만족되지 않음을 확인한 바 있으며, 일반화 쌍곡분포가 보다 현실을 잘 반영하는 모형임을 확인하였다. 또한, Hu와 Kercheval (2007)은 6년간의 S&P500 지수의 분석에서 정규분포는 VaR (value at risk)을 과소 추정하는 반면, 일반화 쌍곡분포는 잘 적합함을 확인하였다. 일반화 쌍곡분포는, Barndorff-Nielsen (1977)이 처음 소개한 분포로, 첨도가 큰 특징을 가지는 금융 자료의 적합에 유용한 분포이다. 본 연구에서는 일반화 쌍곡분포를 모분포로 하는 선형 포트폴리오의 위험측도를 추정한다. 위험측도로는 VaR과 ES (expected shortfall)를 고려하였으며, 추정 방법으로는 안장점근사를 사용하였다. 안장점근사는 소표본에서도 정확한 근사를 제공하는 근사법으로 알려져 있다. 모의실험을 통해 위험측도에 대한 안장점근사의 정도가 매우 우수함을 확인하였다.

• 대한수학회보
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• 제50권4호
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• pp.1127-1144
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• 2013

In this paper, we consider the error estimates of the numerical solutions of a class of fourth order linear-quadratic elliptic optimal control problems by using mixed finite element methods. The state and co-state are approximated by the order $k$ Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise polynomials of order $k(k{\geq}1)$. $L^2$ and $L^{\infty}$-error estimates are derived for both the control and the state approximations. These results are seemed to be new in the literature of the mixed finite element methods for fourth order elliptic control problems.

• ETRI Journal
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• 제39권1호
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• pp.1-12
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• 2017

In this paper, we present a new approach for the progressive compression of three-dimensional (3D) mesh geometry using redundant frame dictionaries and sparse approximation techniques. We construct the proposed frames from redundant linear combinations of the eigenvectors of a combinatorial mesh Laplacian matrix. We achieve a sparse synthesis of the mesh geometry by selecting atoms from a frame using matching pursuit. Experimental results show that the resulting rate-distortion performance compares favorably with other progressive mesh compression algorithms in the same category, even when a very simple, sub-optimal encoding strategy is used for the transmitted data. The proposed frames also have the desirable property of being able to be applied directly to a manifold mesh having arbitrary topology and connectivity types; thus, no initial remeshing is required and the original mesh connectivity is preserved.

• Communications for Statistical Applications and Methods
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• 제16권4호
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• pp.713-722
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• 2009

The estimation of odds ratio and corresponding confidence intervals for case-control data have been done by traditional generalized linear models which assumed that the logarithm of odds ratio is linearly related to risk factors. We adapt a lower-dimensional approximation of Gu and Kim (2002) to provide a faster computation in nonparametric method for the estimation of odds ratio by allowing flexibility of the estimating function and its Bayesian confidence interval under the Bayes model for the lower-dimensional approximations. Simulation studies showed that taking larger samples with the lower-dimensional approximations help to improve the smoothing spline estimates of odds ratio in this settings. The proposed method can be used to analyze case-control data in medical studies.

• 응용통계연구
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• 제27권5호
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• pp.809-818
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• 2014

다변량 왜정규분포는 다변량 정규분포를 포함하는 분포로 최근 많은 응용분야에서 활용되고 있다. 본 논문에서는 다변량 왜정규분포를 기반으로 하는 선형결합통계량의 분포함수에 대한 안장점근사를 다루었다. 이는 단변량 왜정규분포 기반 표본평균에 대한 Na와 Yu (2013)의 결과를 선형결합 및 다변량의 경우로 확장한 것이다. 모의실험과 실제자료분석을 통해 제안된 근사법의 유용성과 정확도를 확인하였다.

• 대한수학회지
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• 제37권6호
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• pp.1031-1042
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• 2000

The equations prescribed in Ω⊂R(sup)n are called loaded, if they contain some operations of the traces of desired solution on manifolds (of dimension which is strongly less than n) from closure Ω. These equations result from approximations of nonlinear equations by linear ones, in the problems of optimal control when the control when the control actions depends on a part of independent variables, in investigations of the inverse problems and so on. In present work we study the nonlocal boundary value problems for first-order loaded differential operator equations. Criterion of unique solvability is established. We illustrate the obtained results by examples.