• Journal of the military operations research society of Korea
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• v.24 no.1
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• pp.146-156
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• 1998

Cholesky factorization is known to be inefficient to problems with dense column and network problems in interior point methods. We use the conjugate gradient method and preconditioners to improve the convergence rate of the conjugate gradient method. Several preconditioners were applied to LPABO 5.1 and the results were compared with those of CPLEX 3.0. The conjugate gradient method shows to be more efficient than Cholesky factorization to problems with dense columns and network problems. The incomplete Cholesky factorization preconditioner shows to be the most efficient among the preconditioners.

• Journal of Korean Society of Transportation
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• v.18 no.5
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• pp.99-107
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• 2000

Path-based assignment(PBA) is valuable to dynamic traffic control and routing in integrated ITS framework. As one of widely studied PBA a1gorithms, Gradient Projection(GP) a1gorithm typically fields rapid convergence to a neighborhood of an optimal solution. But once it comes near a solution, it tends to slow down. To overcome this problem, we develop more efficient path-based assignment algorithm by combining Conjugate Gradient method with GP algorithm. It determines more accurate moving direction near a solution in order to gain a significant advantage in speed of convergence. Also this algorithm is applied to the Sioux-Falls network and verified its efficiency. Then we demonstrate that this type of method is very useful in improving speed of convergence in the case of user equilibrium problem.

• Proceedings of the KOR-KST Conference
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• 1999.10a
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• pp.65-70
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• 1999

• 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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.12
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• pp.1715-1725
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• 1998

A two-dimensional transient inverse heat conduction problem involving the estimation of the unknown location, ($X^*$, $Y^*$), and timewise varying unknown strength, $G({\tau})$, of a line heat source embedded inside a rectangular bar with insulated boundaries has been solved simultaneously. The regular conjugate gradient method, RCGM and the modified conjugate gradient method, MCGM with adjoint equation, are used alternately to estimate the unknown strength $G({\tau})$ of the source term, while the parameter estimation approach is used to estimate the unknown location ($X^*$, $Y^*$) of the line heat source. The alternate use of the regular and the modified conjugate gradient methods alleviates the convergence difficulties encountered at the initial and final times (i.e ${\tau}=0$ and ${\tau}={\tau}_f$), hence stabilizes the computation and fastens the convergence of the solution. In order to examine the effectiveness of this approach under severe test conditions, the unknown strength $G({\tau})$ is chosen in the form of rectangular, triangular and sinusoidal functions.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.2
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• pp.93-99
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• 1998

Parabolic approximation and sponge layer are applied as open boundary condition for elliptic finite difference wave model. Generalized conjugate gradient method is used as a solution procedure. Using parabolic approximation a large part of spurious reflection is removed at the spherical shoal experiment and sponge layer boundary condition needs more than 2 wave lengths of sponge layer to give similar results. Simulating the propagation of waves on a rectangular harbor, it is identified that iterative scheme can be applied easily for the non-rectangular computational region.

• Geophysics and Geophysical Exploration
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• v.10 no.2
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• pp.147-153
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• 2007

The conjugate gradient (CG) method is one of the most efficient algorithms for solving a linear system of equations. In addition to being used as a linear equation solver, it can be applied to a least-squares problem. When the CG method is applied to large-scale three-dimensional inversion of magnetotelluric data, two approaches have been pursued; one is the linear CG inversion in which each step of the Gauss-Newton iteration is incompletely solved using a truncated CG technique, and the other is referred to as the nonlinear CG inversion in which CG is directly applied to the minimization of objective functional for a nonlinear inverse problem. In each procedure we only need to compute the effect of the sensitivity matrix or its transpose multiplying an arbitrary vector, significantly reducing the computational requirements needed to do large-scale inversion.

• Journal of the Korea Society of Computer and Information
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• v.3 no.2
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• pp.139-146
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• 1998

This paper proposes a regularized iterative image restoration using method of conjugate gradient considering a priori information. Compared with conventional regularized method of conjugate gradient, this method has merits to prevent the artifacts by ringing effects and the partial magnification of the noise in the course of restoring the image degraded by blur and additive noise. Proposed method applies the constraints to accelerate the convergence ratio near the edge portions, and the regularized parameter suppresses the magnification of the noise. As experimental results, I show the superior convergence ratio and the suppression by the artifacts of the proposed method compared with conventional methods.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.1
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• pp.22-28
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• 1990

This paper is a study on the reduction of computation time in case of nonlinear magnetic field analysis by finite element method and Newton-Raphson method. For the purpose, the nonlinear convergence equation is computed by the conjugate gradient method which is known to be applicable to symmetric positive definite matrix equations only. As the results, we can not prove mathematically that the system Jacobian is positive definite, but when we applied this method, the diverging case did not occur. And the computation time is reduced by 25-55% and 15-45% in comparison with the case of direct and successive over-relaxation method, respectively. Therefore, we proved the utility of conjugate gradient method.

• Proceedings of the KIEE Conference
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• 1990.07a
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• pp.139-142
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• 1990

This paper presents a new approach to optimal power flow (OPF) problem using conjugate gradient method, using this method. We can obtain initial feasible solution and lagrangian multiplier without calculation of matrix inversion.Test experiment shows a desiriable result and a stable convergence characteristic.