• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.239-251
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• 2007

We show how the minimization can be used to solve the quadratic matrix equation and then compare two different types of conjugate gradient method which are Polak and Ribi$\acute{e}$re version and Fletcher and Reeves version. Finally, some results of the global and local convergence are shown.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.9
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• pp.1985-1997
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• 1997

This paper proposed a regularized iterative image restoration by using method of conjugate gradient. Compared with conventional iterative methods, method of conjugate gradient has a merit to converte toward a solution as a super-linear convergence speed. But because of those properties, there are several artifacts like ringing effects and the partial magnification of the noise in the course of restoring the images that are degraded by a defocusing blur and additive noise. So, we proposed the regularized method of conjugate gradient applying constraints. By applying the projectiong constraint and regularization parameter into that method, it is possible to suppress the magnification of the additive noise. As a experimental results, we showed the superior convergence ratio of the proposed mehtod compared with conventional iterative regularized methods.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.4
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• pp.191-197
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• 2021

To calculate the induced charge of atoms in molecular dynamics, linear equations for the induced charges need to be solved. As induced charges are determined at each time step, the process involves considerable computational costs. Hence, an efficient method for calculating the induced charge distribution is required when analyzing large systems. This paper introduces the Uzawa method for solving saddle point problems, which occur in linear systems, for the solution of the Lagrange equation with constraints. We apply the accelerated Uzawa algorithm, which reduces computational costs noticeably using the Schur complement and preconditioned conjugate gradient methods, in order to overcome the drawback of the Uzawa parameter, which affects the convergence speed, and increase the efficiency of the matrix operation. Numerical models of molecular dynamics in which two gold nanoparticles are placed under external electric fields reveal that the proposed method provides improved results in terms of both convergence and efficiency. The computational cost was reduced by approximately 1/10 compared to that for the Gaussian elimination method, and fast convergence of the conjugate gradient, as compared to the basic Uzawa method, was verified.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.73-81
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• 2013

In this paper, an efficient hybrid nonlinear conjugate gradient method is proposed to solve general unconstrained optimization problems on the basis of CD method [2] and DY method [5], which possess the following property: the sufficient descent property holds without any line search. Under the Wolfe line search conditions, we proved the global convergence of the hybrid method for general nonconvex functions. The numerical results show that the hybrid method is especially efficient for the given test problems, and it can be widely used in scientific and engineering computation.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.3
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• pp.364-373
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• 1999

A combination of conjugate gradient and Levenberg-Marquardt method is used to estimate the spatially varying scattering coefficient, ${\sigma}(r)$, in the solid and hollow spheres by utilizing the measured transmitted beams from the solution of an inverse analysis. The direct radiation problem associated with the inverse problem is solved by using the $S_{12}-approximation$ of the discrete ordinates method. The accuracy of the computations increased when the results from the conjugate gradient method are used as an initial guess for the Levenberg-Marquardt method of minimization. Optical thickness up to ${\tau}_0=3$ is used for the computations. Three different values of standard deviation are considered to examine the accuracy of the solution from the inverse analysis.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.1288-1293
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• 2004

Inverse radiation problems are solved for estimating the boundary conditions such as temperature distribution and wall emissivity in axisymmetric absorbing, emitting and scattering medium, given the measured incident radiative heat fluxes. Various regularization methods, such as hybrid genetic algorithm, conjugate-gradient method and Newton method, were adopted to solve the inverse problem, while discussing their features in terms of estimation accuracy and computational efficiency. Additionally, we propose a new combined approach of adopting the genetic algorithm as an initial value selector, whereas using the conjugate-gradient method and Newton method to reduce their dependence on the initial value.

• Journal of Integrative Natural Science
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• v.1 no.3
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• pp.221-229
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• 2008

본 논문에서는 기존의 개인 식별 방법의 한계를 해결하는 대안으로 떠오르고 있는 생체인식 기술 중 인식률이 뛰어나고 신뢰성 있는 홍채인식 시스템을 구현하고자 한다. 구현을 위하여 신호처리 분야에서 주로 사용되는 wavelet변환으로 계수 특징 값 추출을 하였으며, 인식률을 알아보기 위하여 신경망 기법을 이용하고자 한다. 그러나 신경망 기법에서 주로 사용되는 비선형 최적화기법인 Scale Conjugate Gradient는 최적화 문제점을 해결하기에는 수렴속도가 느리기 때문에 적합하지 않다. 따라서 본 논문에서는 기존 Scale Conjugate Gradient를 보완한 Levenberg-Marquardt Back-Propagation을 홍채인식에 적용하여 구현함으로써 인식율을 높이고자 한다. 적용한 알고리즘 구현으로 해의 수렴정도, 변수 벡터의 변화정도에 따라 크기를 적절히 변화시킴으로써 수렴속도를 개선하고, 효율성과 안정성을 동시에 얻을 수 있었다.

• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.271-278
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• 2017

In this paper, we propose a new conjugate gradient method which possesses the global convergence and apply it to solve inverse problems of the dynamic loads identification. Moreover, we strictly prove the stability and convergence of the proposed method. Two engineering numerical examples are presented to demonstrate the effectiveness and speediness of the present method which is superior to the Landweber iteration method. The results of numerical simulations indicate that the proposed method is stable and effective in solving the multi-source dynamic loads identification problems of practical engineering.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.2
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• pp.276-284
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• 2003

The preconditioned conjugate gradient method is an efficient iterative solution scheme for large size finite element problems. As preconditioning method, we choose an incomplete Cholesky factorization which has efficiency and easiness in implementation in this paper. The incomplete Cholesky factorization mettled sometimes leads to breakdown of the computational procedure that means pivots in the matrix become minus during factorization. So, it is inevitable that a reduction process fur stabilizing and this process will guarantee robustness of the algorithm at the cost of a little computation. Recently incomplete factorization that enhances robustness through increasing diagonal dominancy instead of reduction process has been developed. This method has better efficiency for the problem that has rotational degree of freedom but is sensitive to parameters and the breakdown can be occurred occasionally. Therefore, this paper presents new method that guarantees robustness for this method. Numerical experiment shows that the present method guarantees robustness without further efficiency loss.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.5 no.2
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• pp.84-90
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• 1993

Iterative solution procedure (Conjugate Gradient Method, Panchang et al., 1991) is implemented for solving the complete mild slope equation for the spherical shoal and the coast with detached breakwater. The numerical results agreed well with the experimental data. The disadvantage that mild slope eguation could be solved only for small domains is now overcome by using this solution procedure. Moreover it can be easily applied to the coastal regions with complex geometry and structures, and needs not so much computer time as the conventional models.