• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.5
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• pp.411-420
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• 2009

This study presents an extended finite difference method based on moving least squares(MLS) method for solving potential problems with interfacial boundary. The approximation constructed from the MLS Taylor polynomial is modified by inserting of wedge functions for the interface modeling. Governing equations are node-wisely discretized without involving element or grid; immersion of interfacial condition into the approximation circumvents numerical difficulties owing to geometrical modeling of interface. Interface modeling introduces no additional unknowns in the system of equations but makes the system overdetermined. So, the numbers of unknowns and equations are equalized by the symmetrization of the stiffness matrix. Increase in computational effort is the trade-off for ease of interface modeling. Numerical results clearly show that the developed numerical scheme sharply describes the wedge behavior as well as jumps and efficiently and accurately solves potential problems with interface.

• Journal of the Korean Data and Information Science Society
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• v.27 no.3
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• pp.827-833
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• 2016

In this paper, we propose a deep least squares support vector machine (LS-SVM) for regression problems, which consists of the input layer and the hidden layer. In the hidden layer, LS-SVMs are trained with the original input variables and the perturbed responses. For the final output, the main LS-SVM is trained with the outputs from LS-SVMs of the hidden layer as input variables and the original responses. In contrast to the multilayer neural network (MNN), LS-SVMs in the deep LS-SVM are trained to minimize the penalized objective function. Thus, the learning dynamics of the deep LS-SVM are entirely different from MNN in which all weights and biases are trained to minimize one final error function. When compared to MNN approaches, the deep LS-SVM does not make use of any combination weights, but trains all LS-SVMs in the architecture. Experimental results from real datasets illustrate that the deep LS-SVM significantly outperforms state of the art machine learning methods on regression problems.

• Journal of the Korean Data and Information Science Society
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• v.21 no.3
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• pp.561-567
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• 2010

Multiclassification is typically performed using voting scheme methods based on combining a set of binary classifications. In this paper we use multiclassification method with a hat matrix of least squares support vector machine (LS-SVM), which can be regarded as the revised one-against-all method. To tackle multiclass problems for large data, we use the $Nystr\ddot{o}m$ approximation and the quadratic Renyi entropy with estimation in the primal space such as used in xed size LS-SVM. For the selection of hyperparameters, generalized cross validation techniques are employed. Experimental results are then presented to indicate the performance of the proposed procedure.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.697-712
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• 2011

We present in this paper two versions of a general correction procedure applied to a classical linear iterative method. This gives us the possibility, under certain assumptions, to obtain an extension of it to inconsistent linear least-squares problems. We prove that some well known extended projection type algorithms from image reconstruction in computerized tomography fit into one or the other of these general versions and are derived as particular cases of them. We also present some numerical experiments on two phantoms widely used in image reconstruction literature. The experiments show the importance of these extension procedures, reflected in the quality of reconstructed images.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.59-80
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• 2003

An incomplete factorization method for preconditioning symmetric positive definite matrices is introduced to solve normal equations. The normal equations are form to solve linear least squares problems. The procedure is based on a block incomplete Cholesky factorization and a multilevel recursive strategy with an approximate Schur complement matrix formed implicitly. A diagonal perturbation strategy is implemented to enhance factorization robustness. The factors obtained are used as a preconditioner for the conjugate gradient method. Numerical experiments are used to show the robustness and efficiency of this preconditioning technique, and to compare it with two other preconditioners.

• Computers and Concrete
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• v.13 no.2
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• pp.173-185
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• 2014

Multivariate analysis is a statistical technique that investigates relationship between multiple predictor variables and response variable and it is a very commonly used statistical approach in cement and concrete industry. During model building stage, however, many predictor variables are included in the model and possible collinearity problems between these predictors are generally ignored. In this study, use of partial least squares (PLS) analysis for evaluating the relationships among the cement and concrete properties is investigated. This regression method is known to decrease the model complexity by reducing the number of predictor variables as well as to result in accurate and reliable predictions. The experimental studies showed that the method can be used in the multivariate problems of cement and concrete industry effectively.

• The Journal of the Acoustical Society of Korea
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• v.25 no.2E
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• pp.43-48
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• 2006

Abstract-Using the recursive generalized eigendecomposition method, we develop a recursive form solution to the data least squares (DLS) problem, in which the error is assumed to lie in the data matrix only. Simulations demonstrate that DLS outperforms ordinary least square for certain types of deconvolution problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.5
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• pp.577-588
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• 2011

This paper provides a novel extended Moving Least Squares(MLS) difference method for the potential problem with weak and strong discontinuities. The conventional MLS difference method is enhanced with jump functions such as step function, wedge function and scissors function to model discontinuities in the solution and the derivative fields. When discretizing the governing equations, additional unknowns are not yielded because the jump functions are decided from the known interface condition. The Poisson type PDE's are discretized by the difference equations constructed on nodes. The system of equations built up by assembling the difference equations are directly solved, which is very efficient. Numerical examples show the excellence of the proposed numerical method. The method is expected to be applied to various discontinuity related problems such as crack problem, moving boundary problem and interaction problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.4
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• pp.493-499
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• 2007

The Taylor expansion expresses a differentiable function and its coefficients provide good approximations for the given function and its derivatives. In this study, m-th order Taylor Polynomial is constructed and the coefficients are computed by the Moving Least Squares method. The coefficients are applied to the governing partial differential equation for solid problems including crack problems. The discrete system of difference equations are set up based on the concept of point collocation. The developed method effectively overcomes the shortcomings of the finite difference method which is dependent of the grid structure and has no approximation function, and the Galerkin-based meshfree method which involves time-consuming integration of weak form and differentiation of the shape function and cumbersome treatment of essential boundary.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.5A
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• pp.457-465
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• 2009

This study presents a moving least squares (MLS) finite difference method for solving elastic crack problems with stress singularity at the crack tip. Near-tip functions are intrinsically employed in the MLS approximation to model near-tip field inducing singularity in stress field. employment of the functions does not lose the merit of the MLS Taylor polynomial approximation which approximates the derivatives of a function without actual differentiating process. In the formulation of crack problem, computational efficiency is considerably improved by taking the strong formulation instead of weak formulation involving time consuming numerical quadrature Difference equations are constructed on the nodes distributed in computational domain. Numerical experiments for crack problems show that the intrinsically enriched MLS finite difference method can sharply capture the singular behavior of near-tip stress and accurately evaluate stress intensity factors.