• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.93-98
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• 1991

An improved and flexible matrix algorithm for solving interlinked separation problems which is based on the homotopy continuation method has been developed. A flexible model of the interlinked stream in standardized matrix form and JACOBIAN generation I algorithm for homotopy continuation are suggested. Also DOF analysis is performed for easy-understanding of equation based simulation of complex column systems. The Algorithm is tested on several problems of interlinked separation processes and some of results are documented.

• 한국항공우주학회지
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• 제44권7호
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• pp.620-628
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• 2016

호모토피 알고리즘은 비선형성이 강하거나 다수의 최적해가 존재하는 비선형 최적제어 문제에서 점진적으로 비선형 항으로 고려하게 해줌으로써 강건하게 전역의 최적해를 구할 수 있는 방법이다. 본 논문에서는 초기 추정치에 둔감한 SBS 알고리즘과 호모토피 알고리즘을 결합한 비선형 최적제어 알고리즘을 제시하였다. 이러한 접근방식은 저추력 궤적최적화 문제와 같이 비선형성이 강한 문제의 최적해를 구하는데 효과적이다. 또한, 비선형성이 강한 문제들은 종종 다수 국소 해가 존재하게 되는데, 이러한 경우에 SBS-호모토피 방법은 점진적으로 전역해를 찾는 것을 가능하게 한다.

• Steel and Composite Structures
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• 제17권1호
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• pp.123-131
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• 2014

In this paper we have considered the vibration of parametrically excited oscillator with strong cubic positive nonlinearity of complex variable in nonlinear dynamic systems with forcing based on Mathieu-Duffing equation. A new analytical approach called homotopy perturbation has been utilized to obtain the analytical solution for the problem. Runge-Kutta's algorithm is also presented as our numerical solution. Some comparisons between the results obtained by the homotopy perturbation method and Runge-Kutta algorithm are shown to show the accuracy of the proposed method. In has been indicated that the homotopy perturbation shows an excellent approximations comparing the numerical one.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권2호
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• pp.37-49
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• 1999

In this paper we develop a general Homotopy method called the Group Homotopy method to solve the symmetric eigenproblem. The Group Homotopy method overcomes notable drawbacks of the existing Homotopy method, namely, (i) the possibility of breakdown or having a slow rate of convergence in the presence of clustering of the eigenvalues and (ii) the absence of any definite criterion to choose a step size that guarantees the convergence of the method. On the other hand, We also have a good approximations of the largest eigenvalue of a Symmetric matrix from Lanczos algorithm. We apply it for the largest eigenproblem of a very large symmetric matrix with a good initial points.

• 대한수학회지
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• 제44권6호
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• pp.1479-1503
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• 2007

In this paper, we study a strong k-deformation retract derived from a relative k-homotopy and investigate its properties in relation to both a k-homotopic thinning and the k-fundamental group. Moreover, we show that the k-fundamental group of a wedge product of closed k-curves not k-contractible is a free group by the use of some properties of both a strong k-deformation retract and a digital covering. Finally, we write an algorithm for calculating the k-fundamental group of a dosed k-curve by the use of a k-homotopic thinning.

• 한국수학교육학회지시리즈A:수학교육
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• 제25권3호
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• pp.77-100
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• 1987

Let G : R$^n$${\times}$R\longrightarrowR$^n$ be defined by a Homotopy solving a system F($\chi$)=0 of nonlinear equations. For the vector v$\^$k/ with G'(u$\sub$k/)v$\^$k/=0, ∥v$\^$k/∥=1 where uk is one point in Zero Curve let u$\sub$0/$\^$k/=v$\^$k/＋$\tau$v$\^$k/ be the first prediction for the next point u$\^$k+1/, $\tau$$\in$(0, 1). When u$\sub$0/$\^$k/ approaching too losely to some unwanted point. to follow the Zero Curve may occur the returning or cycling. One lion for it is discussed and tile parametrizied Homotopy algorithm for solving F($\chi$)=0 with it been established. Also some theorems by means of the regular value have been discussed for Zero Curves of G(u)=0 and some theorems for algorithm have been obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권1호
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• pp.17-27
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• 2010

In this paper, we apply homotopy perturbation method (HPM) for solving ninth and tenth-order boundary value problems. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed homotopy perturbation method solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this technique over the decomposition method.

• Journal of applied mathematics & informatics
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• 제2권1호
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• pp.41-58
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• 1995

When F(χ)=0 is a system of nonlinear equations, we have established the parametrizied Homotopy algorithm for solving F(χ)=0 and some theorems for algorithm have been obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제4권2호
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• pp.99-110
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• 2000

This paper is devoted to the parallelism of a numerical matrix eigenvalue problem. The eigenproblem arises in a variety of applications, including engineering, statistics, and economics. Especially we try to approach the industrial techniques from mathematical modeling. This paper has developed a parallel algorithm to find all eigenvalues. It is contributed to solve a specific practical problem, a vibration problem in the industry. Also we compare the runtime between the serial algorithm and the parallel algorithm for the given problems.

• Earthquakes and Structures
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• 제9권1호
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• pp.221-232
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• 2015

In this study, Homotopy Perturbation Method (HPM) is used to solve the nonlinear oscillators with damping. We have considered two strong nonlinear equations to show the application of the method. The Runge-Kutta's algorithm is used to obtain the numerical solution for the problems. The method works very well for the whole range of initial amplitudes and does not demand small perturbation and also sufficiently accurate to both linear and nonlinear physics and engineering problems. Finally to show the accuracy of the HPM, the results have been shown graphically and compared with the numerical solution.