• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.475-484
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• 2004

This paper consider the testing problem of grouped heteroscedasticity in the linear regression model. We provide the Lagrange Multiplier(LM), Wald, Likelihood Ratio (LR) test statistis for testing of grouped heteroscedasticity. Monte Carlo experiments are conducted to study the performance of these tests.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.12 s.243
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• pp.1629-1637
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• 2005

Optimum sensitivity analysis (OSA) is the process to find the sensitivity of optimum solution with respect to the parameter in the optimization problem. The prevalent OSA methods calculate the optimum sensitivity as a post-processing. In this research, a simple technique is proposed to obtain optimum sensitivity as a result of the original optimization problem, provided that the optimum sensitivity of objective function is required. The parameters are considered as additional design variables in the original optimization problem. And then, it is endowed with equality constraints to penalize the additional variables. When the optimization problem is solved, the optimum sensitivity of objective function is simultaneously obtained as Lagrange multiplier. Several mathematical and engineering examples are solved to show the applicability and efficiency of the method compared to other OSA ones.

• Journal of the Korean Data and Information Science Society
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• v.8 no.1
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• pp.9-20
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• 1997

Several methods are proposed for optimizing Fourier series estimators with respect to Mean Integrated Square Error metrics. Traditionally, such method have followed. one of two basic strategies; A stopping rules or the rules of determine multipliers. A central hypothesis of this study is that better estimates can be obtained by combining the two strategies. A new multiplier sequence is proposed, which used in conjunction with any of the stopping rules, is shown to improve the performance of estimator which relies solely on a stopping rule.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1993.04a
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• pp.52-56
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• 1993

An efficient method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. The method is based upon the mode synthesis formulation procedure, but does not construct the equations of motion of the combined whole structure compared with the conventional methods. For modal bases of each linear substructure, either fixed or free interface modes can be employed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurate and efficient in calculating transient responses compared with the direct numerical integration method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.10
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• pp.2457-2466
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• 1993

A simple method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. Although the method is based upon the mode synthesis formulation procedure, the equations of the combined whole structure are not constructed compared with the conventional methods. Lagrange multi-pliers are used to enforce the conditions of geometric compatibility between the substructure interfaces and they are treated as external forces on each substructure itself. Substructure eigenvalue problem is defined with the substructure interface free of fixed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurated and efficient in calculating transient responses compared with the direct numerical integration method.

• Structural Engineering and Mechanics
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• v.41 no.5
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• pp.617-632
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• 2012

An isogeometric approach is presented for static analysis of thin plate problems of various geometries. Non-Uniform Rational B-Splines (NURBS) basis function is applied for approximation of the thin plate deflection, as for description of the geometry. The governing equation based on Kirchhoff plate theory, is discretized using the standard Galerkin method. The essential boundary conditions are enforced by the Lagrange multiplier method. Several typical examples of thin plate and thin plate on elastic foundation are solved and compared with the theoretical solutions and other numerical methods. The numerical results show the robustness and efficiency of the proposed approach.

• Journal of the korean Society of Automotive Engineers
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• v.15 no.1
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• pp.81-88
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• 1993

A direct treatment of the min-max type objective function of the dynamic response optimization problem is proposed. Previously, the min-max type objective function was transformed to an artificial design variable and an additional point-wise state variable constraint function was imposed, which increased the complexity of the optimization problem. Especially, the design sensitivity analysis for the augmented Lagrangian functional with the suggested treatment is established by using the adjoint variable method and a computer program to implement the proposed algorithm is developed. The optimization result of the proposed treatment are obtained for three typical problems and compared with those of the previous treatment. It is concluded that the suggested treatment in much more efficient in the computational effort than the previous treatment with giving the similar optimal solutions.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.10a
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• pp.464-469
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• 2005

Optimum sensitivity analysis (OSA) is the process to find the sensitivity of optimum solution with respect to the parameter in the optimization problem. The prevalent OSA methods calculate the optimum sensitivity as a post-processing. In this research, a simple technique is proposed to obtain optimum sensitivity as a result of the original optimization problem, provided that the optimum sensitivity of objective function is required. The parameters are considered as additional design variables in the original optimization problem. And then, it is endowed with equality constraints to penalize the additional variables. When the optimization problem is solved, the optimum sensitivity of objective function is simultaneously obtained as Lagrange multiplier. Several mathematical and engineering examples are solved to show the applicability and efficiency of the method compared to other OSA ones.

• Journal of the Korean Regional Science Association
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• v.35 no.4
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• pp.3-18
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• 2019

This study estimates the levels of the basic and nonbasic activities in five rural centers in Cheongwon County by using the direct survey method and indirect non-survey methods. The economic base multipliers obtained through direct survey method and indirect non-survey methods are compared to find out the advantages and disadvantages of the estimation methods. There are some limitations in applying non-survey methods for economic base estimation. It is found that, among three non-survey methods, multipliers obtained through minimum requirements method are better than other two methods in terms of the theoretical assumption. However, if we use direct survey data and in-commuter/out-commuter data, we can obtain more accurate multiplier estimates.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.42 no.5 s.335
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• pp.23-30
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• 2005

In the construction of an extension field, there is a connection between the polynomial multiplication method and the degree of polynomial. The existing methods, KO and MSK methods, efficiently reduce the complexity of coefficient-multiplication. However, when we construct the multiplication of an extension field using KO and MSK methods, the polynomials are padded with necessary number of zero coefficients in general. In this paper, we propose basic properties of KO and MSK methods and algorithm that can reduce coefficient-multiplications. The proposed algorithm is more reducible than the original KO and MSK methods. This characteristic makes the employment of this multiplier particularly suitable for applications characterized by specific space constrains, such as those based on smart cards, token hardware, mobile phone or other devices.