• The Journal of the Acoustical Society of Korea
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• v.29 no.6
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• pp.374-380
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• 2010

It is known that the problem of FIR filtering with noisy input and output data can be solved by a total least squares (TLS) estimation. It is also known that the performance of the TLS estimation is very sensitive to the ratio between the variances of the input and output noises. In this paper, we propose a convex combination algorithm between the ordinary recursive LS based TLS (RTLS) and the ordinary recursive LS (RLS). This combined algorithm is robust to the noise variance ratio and has almost the same complexity as the RTLS. Simulation results show that the proposed algorithm performs near TLS in noise variance ratio ${\gamma}{\approx}1$ and that it outperforms TLS and LS in the rage of 2 < $\gamma$ < 20. Consequently, the practical workability of the TLS method applied to noisy data has been significantly broadened.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.12
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• pp.2019-2031
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• 2004

The least-squares formulation for rigid-plasticity based on J$_2$-flow rule and infinitesimal theory and its meshfree implementation using moving least-squares approximation are proposed. In the least-squares formulation the squared residuals of the constitutive and equilibrium equations are minimized. Those residuals are represented in a form of first-order differential system using the velocity and stress components as independent variables. For the enforcement of the boundary and frictional contact conditions, penalty scheme is employed. Also the reshaping of nodal supports is introduced to avoid the difficulties due to the severe local deformation near the contact interface. The proposed least-squares meshfree method does not require any structure of extrinsic cells during the whole process of analysis. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are investigated.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.349-372
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• 2015

This paper concerns with exploiting an oblique projection technique to solve a general class of large and sparse least squares problem over symmetric arrowhead matrices. As a matter of fact, we develop the conjugate gradient least squares (CGLS) algorithm to obtain the minimum norm symmetric arrowhead least squares solution of the general coupled matrix equations. Furthermore, an approach is offered for computing the optimal approximate symmetric arrowhead solution of the mentioned least squares problem corresponding to a given arbitrary matrix group. In addition, the minimization property of the proposed algorithm is established by utilizing the feature of approximate solutions derived by the projection method. Finally, some numerical experiments are examined which reveal the applicability and feasibility of the handled algorithm.

• 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.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.299-315
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• 2015

In this paper, we study the first-order system least-squares (FOSLS) spectral method for parabolic partial differential equations. There were lots of least-squares approaches to solve elliptic partial differential equations using finite element approximation. Also, some approaches using spectral methods have been studied in recent. In order to solve the parabolic partial differential equations in parallel, we consider a parallel numerical method based on a hybrid method of the frequency-domain method and first-order system least-squares method. First, we transform the parabolic problem in the space-time domain to the elliptic problems in the space-frequency domain. Second, we solve each elliptic problem in parallel for some frequencies using the first-order system least-squares method. And then we take the discrete inverse Fourier transforms in order to obtain the approximate solution in the space-time domain. We will introduce such a hybrid method and then present a numerical experiment.

• East Asian mathematical journal
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• v.35 no.5
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• pp.569-587
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• 2019

In this paper, we consider a split least-squares characteristic mixed element method for Sobolev equations with a convection term. First, to manipulate both convection term and time derivative term efficiently, we apply a characteristic mixed element method to get the system of equations in the primal unknown and the flux unknown and then get a least-squares minimization problem and a least-squares characteristic mixed element scheme. Finally, we obtain a split least-squares characteristic mixed element scheme for the given problem whose system is uncoupled in the unknowns. We prove the optimal order in $L^2$ and $H^1$ normed spaces for the primal unknown and the suboptimal order in $L^2$ normed space for the flux unknown.

• East Asian mathematical journal
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• v.38 no.3
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• pp.293-319
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• 2022

In this paper, we introduce a higher order split least-squares characteristic mixed element scheme for Sobolev equations. First, we use a characteristic mixed element method to manipulate both convection term and time derivative term efficiently and obtain the system of equations in the primal unknown and the flux unknown. Second, we define a least-squares minimization problem and a least-squares characteristic mixed element scheme. Finally, we obtain a split least-squares characteristic mixed element scheme for the given problem whose system is uncoupled in the unknowns. We establish the convergence results for the primal unknown and the flux unknown with the second order in a time increment.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.91-113
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• 2023

The polytope of tristochastic tensors of degree three, the Latin polytope, has two kinds of extreme points. Those that are at a maximum distance from the barycenter of the polytope correspond to Latin squares. The remaining extreme points are said to be short. The aim of the paper is to determine the geometry of these short extreme points, as they relate to the Latin squares. The paper adapts the Latin square notion of an intercalate to yield the new concept of a cross-intercalate between two Latin squares. Cross-intercalates of pairs of orthogonal Latin squares of degree three are used to produce the short extreme points of the degree three Latin polytope. The pairs of orthogonal Latin squares fall into two classes, described as parallel and reversed, each forming an orbit under the isotopy group. In the inverse direction, we show that each short extreme point of the Latin polytope determines four pairs of orthogonal Latin squares, two parallel and two reversed.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2003.10a
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• pp.15-19
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• 2003

The Total Least Squares (TLS) method is introduced in comparison with the conventional Least Squares (LS) method. The principles and mathematical models for both methods are summarized and the comparison results from their applications to a simple geometric example, fitting a straight line to a set of 2D points are presented. As conceptually reasoned, the results clearly indicate that LS is more susceptible of producing wrong parameters with worse precision rather than TLS. For many applications in surveying, can adjustment computation and parameter estimation based on TLS provide better results.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.271-284
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• 2002

In this paper we consider the robust inference for the parameter of linear regression model based on weighted least squares. First we consider the sequential test of multiple outliers. Next we suggest the way to assign a weight to each observation $(x_i,\;y_i)$ and recommend the robust inference for linear model. Finally, to check the performance of confidence interval for the slope using proposed method, we conducted a Monte Carlo simulation and presented some numerical results and examples.