• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.657-670
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• 2015

In this paper, we provide numerical analysis of so-called Legendre Gauss-Radau and Legendre-Gauss collocation methods for ordinary differential equations. After recasting these collocation methods as Runge-Kutta methods, we prove that the Legendre-Gauss collocation method is equivalent to the well-known Gauss method, while the Legendre-Gauss-Radau collocation method does not belong to the classes of Radau IA or Radau IIA methods in the Runge-Kutta literature. Making use of the well-established theory of Runge-Kutta methods, we study stability and accuracy of the Legendre-Gauss-Radau collocation method. Numerical experiments are conducted to confirm our theoretical results on the accuracy and numerical stability of the Legendre-Gauss-Radau collocation method, and compare Legendre-Gauss collocation method with the Gauss method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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• pp.71-79
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• 1999

We consider multi-step quasi-Newton methods for unconstrained optimization. These methods were introduced by Ford and Moghrabi [1, 2], who showed how interpolating curves could be used to derive a generalization of the Secant Equation (the relation normally employed in the construction of quasi-Newton methods). One of the most successful of these multi-step methods makes use of the current approximation to the Hessian to determine the parameterization of the interpolating curve in the variable-space and, hence, the generalized updating formula. In this paper, we investigate new parameterization techniques to the approximate Hessian, in an attempt to determine a better Hessian approximation at each iteration and, thus, improve the numerical performance of such algorithms.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1103-1113
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• 2011

Gene expression data is obtained through many stages of an experiment and errors produced during the process may cause missing values. Due to the distinctness of the data so called 'small n large p', genes have to be selected for statistical analysis, like classification analysis. For this reason, imputation and gene selection are important in a microarray data analysis. In the literature, imputation, gene selection and classification analysis have been studied respectively. However, imputation, gene selection and classification analysis are sequential processing. For this aspect, we compare the performance of classification methods after imputation and gene selection methods are applied to microarray data. Numerical simulations are carried out to evaluate the classification methods that use various combinations of the imputation and gene selection methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.2
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• pp.171-188
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• 2015

In this paper, the efficient column-wise/row-wise lattice reduction (LR) updating and downdating methods are developed and their complexities are analyzed. The well-known LLL algorithm, developed by Lenstra, Lenstra, and Lov${\acute{a}}$sz, is considered as a LR method. When the column or the row is appended/deleted in the given lattice basis matrix H, the proposed updating and downdating methods modify the preconditioning matrix that is primarily computed for the LR with H and provide the initial parameters to reduce the updated lattice basis matrix efficiently. Since the modified preconditioning matrix keeps the information of the original reduced lattice bases, the redundant computational complexities can be eliminated when reducing the lattice by using the proposed methods. In addition, the rounding error analysis of the proposed methods is studied. The numerical results demonstrate that the proposed methods drastically reduce the computational load without any performance loss in terms of the condition number of the reduced lattice basis matrix.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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• pp.161-197
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• 2020

Total variation minimization is standard in mathematical imaging and there have been numerous researches over the last decades. In order to process large-scale images in real-time, it is essential to design parallel algorithms that utilize distributed memory computers efficiently. The aim of this paper is to illustrate recent advances of domain decomposition methods for total variation minimization as parallel algorithms. Domain decomposition methods are suitable for parallel computation since they solve a large-scale problem by dividing it into smaller problems and treating them in parallel, and they already have been widely used in structural mechanics. Differently from problems arising in structural mechanics, energy functionals of total variation minimization problems are in general nonlinear, nonsmooth, and nonseparable. Hence, designing efficient domain decomposition methods for total variation minimization is a quite challenging issue. We describe various existing approaches on domain decomposition methods for total variation minimization in a unified view. We address how the direction of research on the subject has changed over the past few years, and suggest several interesting topics for further research.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.262-295
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• 2021

This paper introduces mono-implicit general linear methods, a special class of general linear methods, which are implicit in the output solution for the numerical integration of differential algebraic equations. We show how L-stable inherent Runge-Kutta members can be derived. The procedures for implementation have been discussed. The numerical test on the problem considered shows that the methods have improved accuracy when compared to RADAU IIA and the results from MATLAB ode15s, which have been taken as our reference solution.

• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.359-365
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• 1997

Unusual observations can greatly influence the results of least wquares estimation. I propose graphical methods which can detect the influential observations.

• Proceedings of the Membrane Society of Korea Conference
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• 2002.04a
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• pp.23-46
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• 2002

The cryogenic, pressure swing adsorption and membrane methods have been used to separate air into nitrogen and oxygen. The air separation membrane is made of the polymers, of which manufacturing process is complicate and it causes a little high production cost. Polymer membrane has temperature limit in usage and low durability even at moderate temperature. Therefore, inorganic membranes have been studied for years. As formation of unit alumino-silicate membrane, unit cells of membrane were made with a few coating methods. In this study the dipping of substrate into sols, application of vacuum to the opposite side of substrate with coating and rotating of the substrate in the sols were found as good coating memthods to make a uniform coating and to control the thickness of membrane. The membrane coats were examined by SEM and XRD. The sample ESZl-1 was compared with those of samples that prepared by another method. The present developed coating methods could be applied to the various types of zeolite membrane formation, that is A- X-, Y- ZSM- and MCM-types of membranes. Also these membrane forming methods could be applied to formation of catalyst absorbed zeolite membrane, of which zeolite absorb the catalytic metals. The product obtained from these coating methods could be applied to the industrial gas and liquid phase catalytic reaction and separation processes.

• Earthquakes and Structures
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• v.13 no.5
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• pp.497-507
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• 2017

Flooding induced scour has been long recognized as a major hazard to river-crossing bridges. Many studies in recent years have attempted to evaluate the effects of scour on the seismic performance of bridges, and probabilistic frameworks are usually adopted. However, direct and straightforward insight about how foundation scour affects bridges as a type of soil-foundation-structure system is usually understated. In this paper, we provide a comprehensive review of applied methods centering around seismic assessment of scoured bridges considering soil-foundation-structure interaction. When introducing these applied analysis and modeling methods, a simple bridge model is provided to demonstrate the use of these methods as a case study. Particularly, we propose the use of nonlinear modal pushover analysis as a rapid technique to model scoured bridge systems, and numerical validation and application of this procedure are given using the simple bridge model. All methods reviewed in this paper can serve as baseline components for performing probabilistic vulnerability or risk assessment for any river-crossing bridge system subject to flood-induced scour and earthquakes.

• Journal of the Korean Society for Library and Information Science
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• v.17
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• pp.85-103
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• 1989

The purpose of this second one of the two consecutive papers, which carried out for the research, is to evaluate their relative effectiveness regarding instruction with such three presentation methods as video/print+ lecture, print/video, print+lecture/video, with which the library of Duk Sung Women's University applied already for the orientation of the freshmen in 1988. In sum, the major research findings are as follows : First, as the more numerous media were applied for the orientation, the instruction were more effective. Second, it is very interesting to find out that there were wide differences in effectiveness among the three presentation methods applied for the student. Especially, the print+ lecture/video method was more effective in the instruction than the print/video method. Surprisingly, the video/print + lecture method was much more effective than the print+ lecture/video method. With the research findings of this two consecutive papers into consideration, it seems safe to say that the video-tape method was most effective among such three orienting methods as lecture, slide-tape, and video tape, and the video/print+lecture method was most effective among such three presentation methods as video/print+lecture, print/video, and print+lecture/video.