• Journal of Power System Engineering
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• v.7 no.1
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• pp.74-81
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• 2003

A system identification is to estimate the mathematical model on the base of input output data and to measure the output in the presence of adequate input for the controlled system. In the traditional system control field, most identification problems have been thought as estimating the unknown modeling parameters on the assumption that the model structures are fixed. In the system identification, it is possible to estimate the true parameter values by the adjusted least squares method in the input output case of no observed noise, and it is possible to estimate the true parameter values by the total least squares method in the input output case with the observed noise. We suggest the adjusted least squares method as a consistent estimation method in the system identification in the case where there is observed noise only in the output. In this paper the adjusted least squares method has been developed from the least squares method and the efficiency of the estimating results was confirmed by the generating data with the computer simulations.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.95-106
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• 2016

In this paper, according to the classical LSQR algorithm forsolving least squares (LS) problem, an iterative method is proposed for finding the minimum-norm pure imaginary solution of the quaternionic least squares (QLS) problem. By means of real representation of quaternion matrix, the QLS's correspongding vector algorithm is rewrited back to the matrix-form algorthm without Kronecker product and long vectors. Finally, numerical examples are reported that show the favorable numerical properties of the method.

• Journal of the Korean Statistical Society
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• v.4 no.1
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• pp.39-56
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• 1975

Ever since Gauss discussed the least-squares method in 1812 and Bertrand translated Gauss's work in French, the least-squares method has been used for various economic analysis. The justification of the least-squares method was given by Markov in 1912 in connection with the previous discussion by Gauss and Bertrand. The main argument concerned the problem of obtaining the best linear unbiased estimates. In some modern language, the argument can be explained as follow.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.6 s.237
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• pp.860-875
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• 2005

A new meshfree method for the analysis of elasto-plastic deformations is presented. The method is based on the proposed first-order least-squares formulation, to which the moving least-squares approximation is applied. The least-squares formulation for the classical elasto-plasticity and its extension to an incrementally objective formulation for finite deformations are proposed. In the formulation, the equilibrium equation and flow rule are enforced in least-squares sense, while the hardening law and loading/unloading condition are enforced exactly at each integration point. The closest point projection method for the integration of rate-form constitutive equation is inherently involved in the formulation, and thus the radial-return mapping algorithm is not performed explicitly. Also the penalty schemes for the enforcement of the boundary and frictional contact conditions are devised. The main benefit of the proposed method is that any structure of cells is not used during the whole process of analysis. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are presented.

• Proceedings of the KIEE Conference
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• 2002.07d
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• pp.2216-2218
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• 2002

A system identification is to measure the output in the presence of a adequate input for the controlled system and to estimate the mathematical model in the basic of input output data. In the system identification, it is possible to estimate the true parameter values by the adjusted least squares method in the input-output case of no observed noise, and it is possible to estimate the true parameter values by the total least squares method in the input-output case with the observed noise. In recent the adjusted least squares method is suggested as a consistent estimation method in the system identification not with the observed noise input but with the observed noise output. In this paper we have developed the adjusted least squares method from the least squares method and have made certain of the efficiency in comparing the estimating results with the generating data by the computer simulations.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.613-626
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• 2017

For the overdetermined linear system, when both the data matrix and the observed data are contaminated by noise, Total Least Squares method is an appropriate approach. Since an ill-conditioned data matrix with noise causes a large perturbation in the solution, some kind of regularization technique is required to filter out such noise. In this paper, we consider a Dual regularized Total Least Squares problem. Unlike the Tikhonov regularization which constrains the size of the solution, a Dual regularized Total Least Squares problem considers two constraints; one constrains the size of the error in the data matrix, the other constrains the size of the error in the observed data. Our method derives two nonlinear equations to construct the iterative method. However, since the Jacobian matrix of two nonlinear equations is not guaranteed to be nonsingular, we adopt a trust-region based iteration method to obtain the solution.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2004.11a
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• pp.9-16
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• 2004

Performing adjustments where the observation equations involve more than a single measurement are General Least Squares(GLS) and Total Least Squares(TLS). This paper introduces theory of the GLS and TLS and compared experimentally accuracy and efficiency of those through 2D conformal coordinate transformation and 2D affine coordinate transformation. In conclusion, in case of 2D coordinate transformation, GLS can produce a little more accurate and efficient than TLS. In survey fields, The GLS and TLS can be used cooperatively for adjusting the actual coordinate measurements.

• 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 information and communication convergence engineering
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• v.13 no.3
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• pp.215-219
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• 2015

Cells in a culture process transform with time and produce many overlapping cells in their vicinity. We are interested in a separation algorithm for images of overlapping cells taken using a fluorescence optical microscope system during a cell culture process. In this study, all cells are assumed to have an ellipse-like shape. For an ellipse fitting-based method, an improved least squares method is used by decomposing the design matrix into quadratic and linear parts for the separation of overlapping cells. Through various experiments, the improved least squares method (numerically stable direct least squares fitting [NSDLSF]) is compared with the conventional least squares method (direct least squares fitting [DLSF]). The results reveal that NSDLSF has a successful separation ratio with an average accuracy of 95% for two overlapping cells, an average accuracy of 91% for three overlapping cells, and about 82% accuracy for four overlapping cells.

• 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.