• Korean Journal of Mathematics
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• v.7 no.2
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• pp.245-269
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• 1999

Multigrid method and acceleration by conjugate gradient method for first-order system least squares (FOSLS) using bilinear finite elements are developed for various boundary value problems of planar linear elasticity. They are two-stage algorithms that first solve for the displacement flux variable, then for the displacement itself. This paper focuses on solving for the displacement flux variable only. Numerical results show that the convergence is uniform even as the material becomes nearly incompressible. Computations for convergence factors and discretization errors are included. Heuristic arguments to improve the convergences are discussed as well.

• Journal of the Korean Data and Information Science Society
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• v.15 no.2
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• pp.507-513
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• 2004

Least-squares support vector machine (LS-SVM) has been very successful in pattern recognition and function estimation problems for crisp data. In this paper, we propose LS-SVM approach to evaluating fuzzy regression model with multiple crisp inputs and a Gaussian fuzzy output. The proposed algorithm here is model-free method in the sense that we do not need assume the underlying model function. Experimental result is then presented which indicate the performance of this algorithm.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.6 no.4
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• pp.43-52
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• 1986

With increasing of computer use, a least squares method is now widely used in the regression analysis of various data. Unreliable results of regression coefficients due to the floating point of computer and problems of ordinary least squares method are described in detail. To improve these problems, a least squares method using orthogonal function is developed. Also, Comparison and analysis are performed through an example of numerical test, and re-orthogonalization method is used to increase the accuracy. As an example of application, the optimum order of AR process for the time series of monthly flow at the Pyungchang station is determined using Akaike's FPE(Final Prediction Error) which decides optimum degree of AR process. The result shows the AR(2) process is optimum to the series at the station.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.761-781
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• 2014

An exponentially accurate nonconforming spectral element method for elasticity systems with discontinuities in the coefficients and the flux across the interface is proposed in this paper. The method is least-squares spectral element method. The jump in the flux across the interface is incorporated (in appropriate Sobolev norm) in the functional to be minimized. The interface is resolved exactly using blending elements. The solution is obtained by the preconditioned conjugate gradient method. The numerical solution for different examples with discontinuous coefficients and non-homogeneous jump in the flux across the interface are presented to show the efficiency of the proposed method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.501-506
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• 2007

A generalized finite difference method for solving solid mechanics problems such as elasticity and crack problems is presented. The method is constructed in framework of Taylor polynomial based on the Moving Least Squares method and collocation scheme based on the diffuse derivative approximation. The governing equations are discretized into the difference equations and the nodal solutions are obtained by solving the system of equations. Numerical examples successfully demonstrate the robustness and efficiency of the proposed method.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.9-26
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• 2001

In some previous papers the author extended two algorithms proposed by Z. Kovarik for approximate orthogonalization of a finite set of linearly independent vectors from a Hibert space, to the case when the vectors are rows (not necessary linearly independent) of an arbitrary rectangular matrix. In this paper we describe combinations between these two methods and the classical Kaczmarz’s iteration. We prove that, in the case of a consistent least-squares problem, the new algorithms so obtained converge ti any of its solutions (depending on the initial approximation). The numerical experiments described in the last section of the paper on a problem obtained after the discretization of a first kind integral equation ilustrate the fast convergence of the new algorithms. AMS Mathematics Subject Classification : 65F10, 65F20.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.353-363
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• 2013

A variant of the global conjugate gradient method for solving general linear systems with multiple right-hand sides is proposed. This method is called as the global conjugate gradient linear least squares (Gl-CGLS) method since it is based on the conjugate gradient least squares method(CGLS). We present how this method can be implemented for the image deblurring problems with Neumann boundary conditions. Numerical experiments are tested on some blurred images for the purpose of comparing the computational efficiencies of Gl-CGLS with CGLS and Gl-LSQR. The results show that Gl-CGLS method is numerically more efficient than others for the ill-posed problems.

• Korean Journal of Computational Design and Engineering
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• v.9 no.2
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• pp.143-147
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• 2004

To design parts satisfying physical property in the continuous region, we do it in the discrete rectangular mesh points. Then we obtain points data from parts design and usually construct the surface using least squares method. In such case, that surface has an oscillation in the ineffective region which is inadequate for physical phenomena or NC machining. To solve both problems simultaneously, we extend the surface smoothly to have small curvature in the extended region. Up to now, we use the least squares method for the parts design in Color Picture Tube or Color Display Tube but in this paper, we use functions which is easily controllable. This surface has no error within the effective region compared to the least squares method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.2
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• pp.125-140
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• 2010

This paper develops a least-squares approach to the solution of the optimal control problem for the Navier-Stokes equations. We recast the optimality system as a first-order system by introducing velocity-flux variables and associated curl and trace equations. We show that a least-squares principle based on $L^2$ norms applied to this system yields optimal discretization error estimates in the $H^1$ norm in each variable.

• Proceedings of the KIEE Conference
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• 1991.07a
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• pp.691-694
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• 1991

In a discrete parameter estimation system, the standard least squares method shows slow convergence. On the other hand, the weighted least squares method has relatively fast convergence. However, if the input is not sufficiently rich, then gain matrix grows unboundedly. In order to solve these problems, this paper proposes a modified least squares algorithm which prevents gain matrix from growing unboundedly and has fast convergence.