• 산업경영시스템학회지
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• 제33권3호
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• pp.130-136
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• 2010

In this study, we propose a new method for generating candidate solutions based on both the Cauchy and the Gaussian probability distributions in order to use the merit of the solutions generated by these distributions. The Cauchy probability distribution has larger probability in the tail region than the Gaussian distribution. Thus, the Cauchy distribution can yield higher probabilities of generating candidate solutions of large-varied variables, which in turn has an advantage of searching wider area of variable space. On the contrary, the Gaussian distribution can yield higher probabilities of generating candidate solutions of small-varied variables, which in turn has an advantage of searching deeply smaller area of variable space. In order to compare and analyze the performance of the proposed method against the conventional method, we carried out experiments using benchmarking problems of real valued functions. From the result of the experiment, we found that the proposed method based on the Cauchy and the Gaussian distributions outperformed the conventional one for most of benchmarking problems, and verified its superiority by the statistical hypothesis test.

• 충청수학회지
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• 제21권1호
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• pp.107-116
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• 2008

In this study the k-fold pseudo-Cauchy's method of order k+3 is proposed from the classical Cauchy's method defined by an iteration $x_{n+1}=x_n-{\frac{f^{\prime}(x_n)}{f^{{\prime}{\prime}}(x_n)}}{\cdot}(1-{\sqrt{1-2f(x_n)f^{{\prime}{\prime}}(x_n)/f^{\prime}(x_n)^2}})$. The convergence behavior of the asymptotic error constant is investigated near the corresponding simple zero. A root-finding algorithm with the k-fold pseudo-Cauchy's method is described and computational examples have successfully confirmed the current analysis.

• 대한수학회논문집
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• 제16권3호
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• pp.487-508
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• 2001

We consider the Cauchy problem for Laplacian. Using the single layer representation, we obtain an equivalent system of boundary integral equations. We show the singular values of the ill-posed Cauchy operator decay exponentially, which means that a small error is exponentially amplified in the solution of the Cauchy problem. We show the decaying rate is dependent on the geometry of he domain, which provides the information on the choice of numerically meaningful modes. We suggest a pseudo-inverse regularization method based on singular value decomposition and present various numerical simulations.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.661-667
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• 2013

In this paper we propose the iterated projection method for the approximate solution of an integro-differential equations with Cauchy kernel in $L^2([-1,1],\mathbb{C})$ using Legendre polynomials. We prove the convergence of the method. A system of linear equations is to be solved. Numerical examples illustrate the theoretical results.

• Korean Journal of Mathematics
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• 제17권1호
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• pp.91-102
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• 2009

Using the fixed point method, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the 3-variable Cauchy functional equation.

• 한국정보과학회논문지:소프트웨어및응용
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• 제37권8호
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• pp.591-598
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• 2010

본 논문에서는 연속형 최적화 문제를 위한 타부 탐색에서 후보 해를 생성하기 위해 사용되는 정규 분포의 단점을 보완하기 위하여 코시 확률 분포에 기초한 후보 해 생성 방법을 제안하였다. 코시 확률 분포는 평균 및 분산 등이 무한대인 확률 분포이며, 분포의 꼬리 부분의 확률이 정규 분포에 비하여 상대적으로 크다. 따라서 코시 분포를 사용하면 변수의 변화가 큰 후보 해가 생성될 확률이 높기 때문에 보다 넓은 변수 공간을 탐색할 수 있는 장점이 있다. 코시 확률 분포를 사용한 타부 탐색의 성능을 기존의 정규 분포를 사용한 방법과 비교 분석하기 위하여 실변수 함수로 구성된 벤치마킹 문제에 적용하여 실험을 실행하였다. 실험 결과를 통해 볼 때, 실험에 사용한 모든 함수에 대하여 코시 분포를 사용한 방법이 보다 나은 결과를 나타냈으며, 또한 통계적 가설 검정을 통하여 코시 확률 분포의 우수성을 입증하였다.

• 한국전산구조공학회논문집
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• 제20권2호
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• pp.127-136
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• 2007

본 논문에서는 비동질 반무한 평면에 대한 비례경계유한요소법의 식을 유도하고 수치예제를 해석하였다. 비례경계유한 요소법은 편미분 방정식을 경계방향으로는 유한요소와 같은 근사를 통해서 약화시키고 방사방향으로는 정확해를 사용하는 반 해석적인 방법으로, 방사방향으로 멱함수를 따라 탄성계수가 변화되는 반무한 평면에 대해서 관계식을 가상일의 원리에 근거하여 새로이 유도하였다. 이 과정에서 반무한평면의 거동이 Euler-Cauchy방정식을 따름을 보이고, 기존의 동질 반무한평면의 해석시 도입되던 로그모드가 비동질 반무한 평면의 해석에는 유효하지 않음을 보였다. 수치예제를 통하여 유도된 식이 타당한 거동을 보임을 증명하고 이 접근법이 실제 공학적 문제의 해결에 있어서 유용함을 보였다.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.895-904
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• 2000

The contact problem of two elastic bodies of arbitrary shape with a general kernel form, investigated from Hertz problem, is reduced to an integral equation of the second kind with Cauchy kernel. A numerical method is adapted to determine the unknown potential function between the two surfaces under certain conditions. Many cases are derived and discussed from the work.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권4호
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• pp.347-355
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• 2023

For numerical evaluation of Cauchy principal value integrals, we present a simple rational function with a parameter satisfying some reasonable conditions. The proposed rational function is employed in coordinate transformation for accelerating the accuracy of the Gauss quadrature rule. The efficiency of the proposed rational transformation method is demonstrated by the numerical result of a selected test example.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.267-281
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• 2022

Herein, an algorithm for efficient evaluation of oscillatory Fourier-integrals with Jacobi-Cauchy type singularities is suggested. This method is based on the use of the traditional Clenshaw-Curtis (CC) algorithms in which the given function is approximated by the truncated Chebyshev series, term by term, and the oscillatory factor is approximated by using Bessel function of the first kind. Subsequently, the modified moments are computed efficiently using the numerical steepest descent method or special functions. Furthermore, Algorithm and programming code in MATHEMATICA^® 9.0 are provided for the implementation of the method for automatic computation on a computer. Finally, selected numerical examples are given in support of our theoretical analysis.