• Journal of the Korean Statistical Society
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• v.29 no.3
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• pp.361-373
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• 2000

A simple and efficient algorithm is introduced for generalized least squares estimation under nonnegativity constraints in the components of the parameter vector. This algorithm gives the exact solution to the estimation problem within a finite number of pivot operations. Besides an illustrative example, an empirical study is conducted for investigating the performance of the proposed algorithm. This study indicates that most of problems are solved in a few iterations, and the number of iterations required for optimal solution increases linearly to the size of the problem. Finally, we will discuss the applicability of the proposed algorithm extensively to the estimation problem having a more general set of linear inequality constraints.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.471-479
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• 2008

Let $R\;{\in}\;C^{m{\times}m}$ and $S\;{\in}\;C^{n{\times}n}$ be nontrivial unitary involutions, i.e., $R^*\;=\;R\;=\;R^{-1}\;{\neq}\;I_m$ and $S^*\;=\;S\;=\;S^{-1}\;{\neq}\;I_m$. We say that $G\;{\in}\;C^{m{\times}n}$ is a generalized reflexive matrix if RGS = G. The set of all m ${\times}$ n generalized reflexive matrices is denoted by $GRC^{m{\times}n}$. In this paper, an efficient method for the least squares solution $X\;{\in}\;GRC^{m{\times}n}$ of the matrix equation AXB = D with arbitrary coefficient matrices $A\;{\in}\;C^{p{\times}m}$, $B\;{\in}\;C^{n{\times}q}$and the right-hand side $D\;{\in}\;C^{p{\times}q}$ is developed based on the canonical correlation decomposition(CCD) and, an explicit formula for the general solution is presented.

• Proceedings of the KIPE Conference
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• 2018.11a
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• pp.175-176
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• 2018

This paper presents a method to estimate the parameter of permanent magnet synchronous motor using a least squares method. The approximate solution of the linear simultaneous equations is obtained by the pseudoinverse least squares method of the input current and output voltage data of the current controller. It is possible to obtain the current response of the same bandwidth to the general control target by using the Pole-zero Cancellation technique. This paper verifies the performance of the proposed method by comparing the results of estimation of parameters of different motors by simulation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.2C
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• pp.255-261
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• 2004

The problem of geolocation using multiple satellites is to determine the position of a transmitter located on the Earth by processing received signals. The specific problem addressed in this paper is that of estimating the position of a stationary transmitter located on or above the Earth's surface from measured time difference of arrivals (TDOA) by a geostationary orbiting (GSO) satellite and a low earth orbiting (LEO) satellite. The proposed geolocation method is based on the total least squares (TLS) algorithm. Under erroneous positions of the satellites together with noisy TDOA measurements, the TLS algorithm provides a better solution. By running Monte-Carlo simulations, the proposed method is compared with the ordinary least squares (LS) approach.

• 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.

• East Asian mathematical journal
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• v.14 no.2
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• pp.399-410
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• 1998

In [3], Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated-linear systems. In this work, we present computational experiments of W-cycle multigrid method. Computational experiments show that the convergence is uniform as the parameter, $\nu$, goes to 1/2.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.631-642
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• 2016

This article deals with one-dimension backward heat conduction problem (BHCP). A new approach based on least squares support vector machines (LS-SVM) is proposed for obtaining their approximate solutions. The approximate solution is presented in closed form by means of LS-SVM, whose parameters are adjusted to minimize an appropriate error function. The approximate solution consists of two parts. The first part is a known function that satisfies initial and boundary conditions. The other is a product of two terms. One term is known function which has zero boundary and initial conditions, another term is unknown which is related to kernel functions. This method has been successfully tested on practical examples and has yielded higher accuracy and stable solutions.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.563-578
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• 2005

In [Z. Cai and B. C. Shin, SIAM J. Numer. Anal. 40 (2002), 307-318], we developed the discrete first-order system least squares method for the second-order elliptic boundary value problem by directly approximating $H(div){\cap}H(curl)-type$ space based on the Helmholtz decomposition. Under general assumptions, error estimates were established in the $L^2\;and\;H^1$ norms for the vector and scalar variables, respectively. Such error estimates are optimal with respect to the required regularity of the solution. In this paper, we study solution methods for solving the system of linear equations arising from the discretization of variational formulation which possesses discrete biharmonic term and focus on numerical results including the performances of multigrid preconditioners and the finite element accuracy.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.9C
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• pp.743-747
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• 2010

This paper presents an iterative adaptive hybrid image restoration algorithm for fast convergence. The local variance, mean, and maximum value are used to constrain the solution space. These parameters are computed at each iteration step using partially restored image at each iteration, and they are used to impose the degree of local smoothness on the solution. The resulting iterative algorithm exhibits increased convergence speed and better performance than typical regularized constrained least squares (RCLS) approach.

• 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.