• 대한수학회논문집
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• 제9권2호
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• pp.439-448
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• 1994

It is known that the steepest descent(SD) method and the conjugate gradient(CG) method [1, 2, 5, 6] converge when these methods are applied to solve linear systems of the form Ax = b, where A is symmetric and positive definite. For some finite difference discretizations of elliptic problems, one gets positive definite matrices that are almost symmetric. Practically, the SD method and the CG method work for these matrices. However, the convergence of these methods is not guaranteed theoretically. The SD method is also called Orthores(1) in iterative method papers. Elman [4] states that the convergence proof for Orthores($\kappa$), with $\kappa$ a positive integer, is not heard. In this paper, we prove that the SD method and the CG method converge when the $\iota$$^2$ matrix norm of the non-symmetric part of a positive definite matrix is less than some value related to the smallest and the largest eigenvalues of the symmetric part of the given matrix.(omitted)

• 대한기계학회논문집B
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• 제28권9호
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• pp.1124-1132
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• 2004

The inverse problem of determining unknown inlet temperature in thermally developing, hydrodynamically developed two phase laminar flow in a parallel plate duct is considered. The inlet temperature profile is determined by measuring temperature in the flow field. No prior information is needed for the functional form of the inlet temperature profile. The inverse convection problem is solved by minimizing the objective function with regularization method. The conjugate gradient method as iterative method and the Tikhonov regularization method are employed. The effects of the functional form of inlet temperature, the number of measurement points and the measurement errors are investigated. The accuracy and efficiency of these two methods are compared and discussed.

• Journal of Electrical Engineering and Technology
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• 제5권4호
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• pp.666-671
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• 2010

Multi-layer perceptron neural networks have been constructed to classify four types of defects in steam generator tubes. Three features are extracted from the signals of the eddy current testing method. These include maximum impedance, phase angle at the point of maximum impedance, and an angle between the point of maximum impedance and the point of half the maximum impedance. Two hundred sets of these features are used for training and assessing the networks. Two approaches are involved to train the networks and to classify the defect type. One is the conjugate gradient method and the other is the Broydon-Fletcher-Goldfarb-Shanno method which is recognized as the most popular algorithm of quasi-Newton methods. It is found from the computation results that the training time of the Broydon-Fletcher-Goldfarb-Shanno method is much faster than that of the conjugate gradient method in most cases. On the other hand, no significant difference of the classification performance between the two methods is observed.

• 한국전산유체공학회지
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• 제3권1호
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• pp.37-45
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• 1998

A new and efficient inverse design method based on the numerical optimization technique has been developed. The 2-D incompressible Navier-Stokes equations are solved for obtaining the objective functions and coupled with the optimization procedure to perform the inverse design. The steepest descent and the conjugate gradient method have been applied to find the searching direction. The golden section method was applied to compute the design variable intervals. It has been found that the airfoil and the pump impellers are well converged to their targeting shapes.

• Computers and Concrete
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• 제12권2호
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• pp.229-241
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• 2013

The objective of this study is to reveal the sufficiency of neural networks (NN) as a securer, quicker, more robust and reliable method to be used in seismic assessment of existing reinforced concrete buildings. The NN based approach is applied as an alternative method to determine the seismic performance of each existing RC buildings, in terms of damage level. In the application of the NN, a multilayer perceptron (MLP) with a back-propagation (BP) algorithm is employed using a scaled conjugate gradient. NN based model wasd eveloped, trained and tested through a based MATLAB program. The database of this model was developed by using a statistical procedure called P25 method. The NN based model was also proved by verification set constituting of real existing RC buildings exposed to 2003 Bingol earthquake. It is demonstrated that the NN based approach is highly successful and can be used as an alternative method to determine the seismic performance of each existing RC buildings.

• 대한기계학회논문집B
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• 제29권8호
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• pp.903-910
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• 2005

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 finite-difference 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 that adopts the hybrid genetic algorithm as an initial value selector and uses the finite-difference Newton method as an optimization procedure.

• 한국지능시스템학회논문지
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• 제21권1호
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• pp.12-18
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• 2011

본 논문에서는 RBF 뉴럴 네트워크에서 은닉층 활성함수에 Interval type-2 퍼지개념을 적용한 새로운 RBF 뉴럴 네트워크를 설계하였다. 퍼지 시스템 분야에서 불확실한 정보에 대한 Type-1 퍼지집합의 성능을 보안하고자 Type-2 퍼지집합이 제안되었으며, 멤버쉽함수 안에 다시 멤버쉽함수를 생성함으로써 불확실한 정보를 좀 더 효과적으로 다루고자 하였다. 따라서 본 논문에서는 RBF 뉴럴 네트워크의 은닉층 활성함수에 type-2 퍼지집합의 개념을 적용하여 불확실한 정보에 대한 모델 성능을 개선하고자 하였다. 나아가 연결가중치를 상수항이 아닌 1차식으로 구성된 다항식을 사용하여 최종출력을 입력-출력의 관계식으로 표현하였다. 연결가중치는 기존의 경사하강법(Gradient Descent Method; GDM) 대신 conjugate gradient method(CGM)을 사용하여 파라미터를 동조하고, 은닉층의 활성함수는 공간탐색 진화 알고리즘(Space Search Evolutionary Algorithm; SSEA)을 이용하여 가우시안 함수의 중심점 및 분포상수를 동조하여 모델의 성능을 개선시킨다. 제안된 모델의 성능을 평가하기 위해 가스로 시계열 데이터를 사용하였으며, 결과를 기존 모델과 비교하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권1호
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• pp.1-13
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• 2018

Boosting, one of the most successful algorithms for supervised learning, searches the most accurate weighted sum of weak classifiers. The search corresponds to a convex programming with non-negativity and affine constraint. In this article, we propose a novel Conjugate Gradient algorithm with the Modified Polak-Ribiera-Polyak conjugate direction. The convergence of the algorithm is proved and we report its successful applications to boosting.

• 호남수학학술지
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• 제17권1호
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• pp.129-140
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• 1995

• Journal of Electrical Engineering and Technology
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• 제4권3호
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• pp.365-369
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• 2009

Identification is considered to be among the main applications of inverse theory and its objective for a given physical system is to use data which is easily observable, to infer some of the geometric parameters which are not directly observable. In this paper, a parameter identification method using inverse problem methodology is proposed. The minimisation of the objective function with respect to the desired vector of design parameters is the most important procedure in solving the inverse problem. The conjugate gradient method is used to determine the unknown parameters, and Tikhonov's regularization method is then used to replace the original ill-posed problem with a well-posed problem. The simulation and experimental results are presented and compared.