• 한국지능시스템학회논문지
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• 제18권4호
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• pp.543-548
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• 2008

This paper is to investigate the existence theorem for the semilinear fuzzy integrodifferential equation in $E_N$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_N$. Main tool is successive iteration method.

• 한국지능시스템학회:학술대회논문집
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• 한국지능시스템학회 2008년도 춘계학술대회 학술발표회 논문집
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• pp.26-28
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• 2008

This paper is to investigate the existence theorem for the semilinear fuzzy integrodifferential equation in ${E_N}$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in ${E_N}$. Main tool is successive iteration method.

• Journal of information and communication convergence engineering
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• 제10권1호
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• pp.66-70
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• 2012

Conformal mapping has been a familiar tool of science and engineering for generations. Determination of a conformal map from the unit disk onto the Jordan region is reduced to solving the Theodorsen equation, which is an integral equation for boundary correspondence functions. There are many methods for solving the Theodorsen equation. It is the goal of numerical conformal mapping to find methods that are at once fast, accurate, and reliable. In this paper, we analyze Niethammer’s solution based on successive over-relaxation (SOR) iteration and Wegmann’s solution based on Newton iteration, and compare them to determine which one is more effective. Through several numerical experiments with these two methods, we can see that Niethammer’s method is more effective than Wegmann’s when the degree of the problem is low and Wegmann’s method is more effective than Niethammer’s when the degree of the problem is high.

• 대한전자공학회논문지
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• 제26권2호
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• pp.41-55
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• 1989

기하 광학(GO)의 반복에 의한 회절파 계산을 제안하였다. 쐐기형 산란체에 전원이 주어졌을때, 그 GO해는 반공간 문제의 해에 명암 경계를 결정하여 얻어진다. 또한, 이러한 GO해의 명암경계를 따라 나타나는 불연소계와 등가인 전원을 계산하여 이를 그 전원으로 하는 새로운 쐐기문제를 생각할 수 있다. 이때, 이 등가전원 문제의 해가 바로 GO해가 필료로 하는 회절파와 같음을 보였다. 또한, 등가전원이 무한공간에서 만드는 파 즉 새로운 쐐기문제이 입사파는 물리광학으로 계산한 회절파와 같은 것임을 보였다. 새로운 쐐기문제에 다시 GO를 적용하여 회절파에 대한 하나의 근사해를 얻었으며 이것을 물리광학에 의한 것과 비교하였다. 또한, 이와 같은 GO반복 적용의 타당성을 보기 위하여 정확한 해가 이미알려져 있는 완전도체쐐기의 GO무한 반복해를 구하여 그 수렴여부를 살폈다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권1호
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• pp.15-28
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• 2018

Recently Machine Learning algorithms are widely used to process Big Data in various applications and a lot of these applications are executed in run time. Therefore the speed of Machine Learning algorithms is a critical issue in these applications. However the most of modern iteration Machine Learning algorithms use a successive iteration technique well-known in Numerical Linear Algebra. But this technique has a very low convergence, needs a lot of iterations to get solution of considering problems and therefore a lot of time for processing even on modern multi-core computers and clusters. Tchebychev iteration technique is well-known in Numerical Linear Algebra as an attractive candidate to decrease the number of iterations in Machine Learning iteration algorithms and also to decrease the running time of these algorithms those is very important especially in run time applications. In this paper we consider the usage of Tchebychev iterations for acceleration of well-known K-Means and SVM (Support Vector Machine) clustering algorithms in Machine Leaning. Some examples of usage of our approach on modern multi-core computers under Apache Spark framework will be considered and discussed.

• East Asian mathematical journal
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• 제24권1호
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• pp.105-110
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• 2008

The aim of this paper is to prove convergence of implicit iteration process to a common fixed point for a finite family of strong successive $\Phi$-pseudocontractive mappings. The results presented in this paper extend and improve the corresponding results of S. S. Chang [On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 313(2006), 273-283], M. O. Osilike[Implicit iteration process for common fixed points of a finite finite family of strictly pseudocontractive maps, Appl. Math. Comput. 189(2) (2007), 1058-1065].

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.383-405
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• 2004

We study the incomprssible Navier Stokes equations for the flow inside contraction geometry. The governing equations are expressed in the vorticity-stream function formulations. A rectangular computational domain is arised by elliptic grid generation technique. The numerical solution is based on a technique of automatic numerical generation of acurvilinear coordinate system by transforming the governing equation into computational plane. The transformed equations are approximated using central differences and solved simultaneously by successive over relaxation iteration. The time dependent of the vorticity equation solved by using explicit marching procedure. We will apply the technique on several irregular-shapes.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.221-233
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• 2016

The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.

• Geomechanics and Engineering
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• 제15권5호
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• pp.1029-1038
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• 2018

A superposition-iteration (S-I) model is proposed to simulate the jet grouting pre-reinforcing impact for a shallow-buried tunnel. The common model is deduced by theoretical (force equilibrium) analysis and then transformed into the numerical formulation. After applying it to an actual engineering problem, the most obvious deficiency was found to be continuous error accumulation, even when the parameters change slightly. In order to address this problem, a superposition-iteration model is developed based on the basic assumption and superposition theory. First, the additional deflection between two successive excavation steps is determined. This is caused by the disappearance of the supporting force in the excavated zone and the soil pressure in the disturbed zone. Consequently, the final deflection can be obtained by repeatedly superposing the additional deflection to the initial deflection in the previous steps. The analytical solution is then determined with the boundary conditions. The superposition-iteration model is thus established. This model was then applied and found to be suitable for real-life engineering applications. During the calculation, the error induced by the ill-conditioned problem of the matrix is easily addressed. The precision of this model is greater compared to previous models. The sensitivity factors and their impact are determined through this superposition-iteration model.

• Journal of the Optical Society of Korea
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• 제2권2호
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• pp.58-63
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• 1998

Cross-talk effects in high-density volume holographic interconnections are investigated using perturbative iteration method of the integral form of Maxwell's wave equation. In this method, the paraxial approximation and negligence of backward scattering introduced in conventional coupled mode theory is not assumed. Interaction geometries consisting of non-coplanar light waves and multiple index gratings are studied. Arbitrary light polarization is considered. Systematic analysis of cross-talk effects due to multiple index gratings is performed in increasing level of diffraction orders corresponding to successive iterations. Some numerical examples are given for first and third order diffraction.