• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.97-107
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• 1994

This paper proposes a numerical method approximating the least squares solution of minimum norm (LSSMN) to the first kind integral equation Kf=g with a special kernel, and then some numerical experiments for this method are provided.

• The Journal of the Acoustical Society of Korea
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• v.26 no.2E
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• pp.63-68
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• 2007

Using the neural network model for oriented principal component analysis (OPCA), we propose a solution to the data least squares (DLS) problem, in which the error is assumed to lie in the data matrix only. In this paper, we applied this neural network model to channel equalization. Simulations show that the neural network based DLS outperforms ordinary least squares in channel equalization problems.

• Economic and Environmental Geology
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• v.28 no.4
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• pp.433-438
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• 1995

The most popular minimization method is based on the least-squares criterion, which uses the $L_2$ norm to quantify the misfit between observed and synthetic data. The solution of the least-squares problem is the maximum likelihood point of a probability density containing data with Gaussian uncertainties. The distribution of errors in the geophysical data is, however, seldom Gaussian. Using the $L_2$ norm, large and sparsely distributed errors adversely affect the solution, and the estimated model parameters may even be completely unphysical. On the other hand, the least-absolute-deviation optimization, which is based on the $L_1$ norm, has much more robust statistical properties in the presence of noise. The solution of the $L_1$ problem is the maximum likelihood point of a probability density containing data with longer-tailed errors than the Gaussian distribution. Thus, the $L_1$ norm gives more reliable estimates when a small number of large errors contaminate the data. The effect of outliers is further reduced by M-fitting method with Cauchy error criterion, which can be performed by iteratively reweighted least-squares method.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.95-112
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• 2006

In this paper, the authors investigate the condition number with their condition numbers for weighted Moore-Penrose inverse and weighted least squares solution of min /Ax - b/M, where A is a rank-deficient complex matrix in $C^{m{\times}n} $ and b a vector of length m in $C^m$, x a vector of length n in $C^n$. For the normwise condition number, the sensitivity of the relative condition number itself is studied, the componentwise perturbation is also investigated.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1061-1071
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• 2009

For real generalized reflexive matrices R, S, i.e., $R^T$ = R, $R^2$ = I, $S^T$ = S, $S^2$ = I, we say that real matrix X is (R,S)-symmetric, if RXS = X. In this paper, an iterative algorithm is proposed to solve the least-squares problem of matrix equation AXB = C with (R,S)-symmetric X. Furthermore, the optimal approximation solution to given matrix $X_0$ is also derived by this iterative algorithm. Finally, given numerical example and its convergent curve show that this method is feasible and efficient.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.355-366
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• 2003

A unified procedure for principal component regression (PCR), partial least squares (PLS) and ordinary least squares (OLS) is proposed. The process gives solutions for PCR, PLS and OLS in a unified and non-iterative way. This enables us to see the interrelationships among the three regression coefficient vectors, and it is seen that the so-called E-matrix in the solution expression plays the key role in differentiating the methods. In addition to setting out the procedure, the paper also supplies a robust numerical algorithm for its implementation, which is used to show how the procedure performs on a real world data set.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.11
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• pp.2312-2321
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• 2002

The first-order least-squares meshfree method for linear elasticity is presented. The conventional and the compatibility-imposed least-squares formulations are studied on the convergence behavior of the solution and the robustness to integration error. Since the least-squares formulation is a type of mixed formulation and induces positive-definite system matrix, by using shape functions of same order for both primal and dual variables, higher rate of convergence is obtained for dual variables than Galerkin formulation. Numerical examples also show that the presented formulations do not exhibit any volumetric locking for the incompressible materials.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1291-1310
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• 2013

This paper develops least-squares pseudo-spectral collocation methods for elliptic boundary value problems having interface conditions given by discontinuous coefficients and singular source term. From the discontinuities of coefficients and singular source term, we derive the interface conditions and then we impose such interface conditions to solution spaces. We define two types of discrete least-squares functionals summing discontinuous spectral norms of the residual equations over two sub-domains. In this paper, we show that the homogeneous least-squares functionals are equivalent to appropriate product norms and the proposed methods have the spectral convergence. Finally, we present some numerical results to provide evidences for analysis and spectral convergence of the proposed methods.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.497-504
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• 2002

In meshless methods, the moving least squares approximation technique is widely used to approximate a solution space because of its useful numerical characters such as non-element approximation, easily controllable smoothness, and others. In this work, a generalized version of the moving least squares method Is introduced to enhance the approximation performance through the Information converning to the derivative of the field variable. The results of numerical tests for approximation verify the improved accuracy of the generalized meshless approximation procedure compared to the conventional moving least squares method. By using this generalized moving least squares method, meshless analysis of thin beam is carried out, and its performance is investigated.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.47-51
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• 2005

Using satellite images, an optimal solution to water motion has been presented in this study. Since temperature patterns are suitable tracers in water motion, Sea Surface Temperature (SST) images of Caspian Sea taken by MODIS sensor on board Terra satellite have been used in this study. Two daily SST images with 24 hours time interval are used as input data. Computation of templates correspondence between pairs of images is crucial within motion algorithms using non-rigid body objects. Image matching methods have been applied to estimate water body motion within the two SST images. The least squares matching technique, as a flexible technique for most data matching problems, offers an optimal spatial solution for the motion estimation. The algorithm allows for simultaneous local radiometric correction and local geometrical image orientation estimation. Actually, the correspondence between the two image templates is modeled both geometrically and radiometrically. Geometric component of the model includes six geometric transformation parameters and radiometric component of the model includes two radiometric transformation parameters. Using the algorithm, the parameters are automatically corrected, optimized and assessed iteratively by the least squares algorithm. The method used in this study, has presented more efficient and robust solution compared to the traditional motion estimation schemes.