• Proceedings of the KSME Conference
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• 2000.04a
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• pp.655-660
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• 2000

This paper presents the construction of consistent coefficient matrix elements for jointed structures using the reduction of flexibility and mass matrices. The reduced flexibility coefficient matrix hat little structural complexity than Guyan's stiffness matrix reduction since the only element of the original matrix, corresponding to the selected nodal degrees of freedom, contributes. The proposed method was applied to building equivalent coefficient matrices for a clamp jointed structure in finite element modal analysis of a cantilevered beam. The theoretical analysis results were compared with those experimental modal analysis, Comparison of both shows good agreement each other.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.667-676
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• 1999

We investigate the effects of omission of initial observations in each individuals in the panel data regression model when the disturbances follow a serially correlated one way error components. We show that the first transformed observation can have a relative large hat matrix diagonal component and a large influence on parameter estimates when the correlation coefficient is large in absolute value.

• 한국지구물리탐사학회:학술대회논문집
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• 2003.11a
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• pp.402-409
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• 2003

Inversion of traveltime requires an efficient algorithm for computing the traveltime as well as its $Frech\hat{e}t$ derivative. We compute the traveltime of the head waves using the damped wave solution in the Laplace domain and then present a new algorithm for calculating the $Frech\hat{e}t$ derivative of the head wave traveltimes by exploiting the numerical structure of the finite element method, the modem sparse matrix technology, and SWEET algorithm developed recently. Then, we use a properly regularized steepest descent method to invert the traveltime of the Marmousi-2 model. Through our numerical tests, we will demonstrate that the refraction tomography with large aperture data can be used to construct the initial velocity model for the prestack depth migration.

• Journal of the Korean Statistical Society
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• v.15 no.2
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• pp.131-142
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• 1986

By using the tool for finding influential cases in regrssion, we investigate teh properties of three types of diagonal elements of the hat matrix in central designs. From thses results, we determine the experimental points at axes ad teh number of replicates as the center and the otherpoints so that the experimental points give approximatly same influences to estimatoe teh response surface.

• Journal of the Korean Data and Information Science Society
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• v.6 no.1
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• pp.63-71
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• 1995

We have consider the study of local influence for smoothing parameter estimates in spline regression model with heteroscedasticity. Practically, generalized cross-validation does not work well in the presence of heteroscedasticity. Thus we have proposed the local influence measure for generalized cross-validation estimates when errors are heteroscedastic. And we have examined effects of diagnostic by above measures through Hyperinflation data.

• Journal of Korea Water Resources Association
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• v.32 no.6
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• pp.657-664
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• 1999

This paper introduced the basic theory of LRCS(Linear Reservoir and Channel System) rainfall runoff model proposed by Korean researchers(Lee and Lee, 1995), and discussed the change of model output according to objective functions in sensitivity analysis and calibration process of model. It proposed "hat" matrix and affluence measures for affluence analysis of parameters in calibration, and investigated relationship between change of model output according to error propagation in parameter estimation, and sensitivity of model output according to variance of model output and change of parameters. Accuracy of parameter estimates was known by analysis of sensitivity coefficient, diagonal element $h_i$ and $D_i$._i$.

• Journal of the Korean Data and Information Science Society
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• v.27 no.2
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• pp.549-557
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• 2016

In this paper we propose multiclassification method for large data sets by ensembling least squares support vector machines (LS-SVM) with principal components instead of raw input vector. We use the revised one-vs-all method for multiclassification, which is one of voting scheme based on combining several binary classifications. The revised one-vs-all method is performed by using the hat matrix of LS-SVM ensemble, which is obtained by ensembling LS-SVMs trained using each random sample from the whole large training data. The leave-one-out cross validation (CV) function is used for the optimal values of hyper-parameters which affect the performance of multiclass LS-SVM ensemble. We present the generalized cross validation function to reduce computational burden of leave-one-out CV functions. Experimental results from real data sets are then obtained to illustrate the performance of the proposed multiclass LS-SVM ensemble.

• Structural Engineering and Mechanics
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• v.13 no.3
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• pp.277-298
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• 2002

In this study, free vibration analysis of Reissner plates on Pasternak foundation is carried out by mixed finite element method based on the G$\hat{a}$teaux differential. New boundary conditions are established for plates on Pasternak foundation. This method is developed and applied to numerous problems by Ak$\ddot{o}$z and his co-workers. In dynamic analysis, the problem reduces to the solution of a standard eigenvalue problem and the mixed element is based upon a consistent mass matrix formulation. The element has four nodes and bending and torsional moments, transverse shear forces, rotations and displacements are the basic unknowns. The element performance is assessed by comparison with numerical examples known from literature. Validity limits of Kirchhoff plate theory is tested by dynamic analysis. Shear locking effects are tested as far as $h/2a=10^{-6}$ and it is observed that REC32 is free from shear locking.

• Journal of the Korean Data and Information Science Society
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• v.21 no.3
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• pp.561-567
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• 2010

Multiclassification is typically performed using voting scheme methods based on combining a set of binary classifications. In this paper we use multiclassification method with a hat matrix of least squares support vector machine (LS-SVM), which can be regarded as the revised one-against-all method. To tackle multiclass problems for large data, we use the $Nystr\ddot{o}m$ approximation and the quadratic Renyi entropy with estimation in the primal space such as used in xed size LS-SVM. For the selection of hyperparameters, generalized cross validation techniques are employed. Experimental results are then presented to indicate the performance of the proposed procedure.

• Communications of Mathematical Education
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• v.36 no.3
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• pp.439-467
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• 2022

The future society requires not only knowledge but also various competencies, including creativity, cooperative spirit and integrated thinking. This research develops a program for integrating mathematics and information science to enhance important mathematical competencies such as problem-solving and communication. This program does not require much prior knowledge, can be motivated using everyday language and easy-to-access tools, and is based on creative problem-solving activities with multilateral cooperation. The usefulness and rigor of mathematics are emphasized as the number of participants increases in the activities, and theoretical principles stem from the matrix theory over finite fields. Moreover, the activity highlights a connection with error-correcting codes, an important topic in information science. We expect that the real-world contexts of this program contribute to enhancing mathematical communication competence and providing an opportunity to experience the values of mathematics and that this program to be accessible to teachers since coding is not included.