• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.411-423
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• 2010

In this paper, a numerical method for singular perturbation problems arising in chemical reactor theory for general singularly perturbed two point boundary value problems with boundary layer at one end(left or right) of the underlying interval is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• IEMEK Journal of Embedded Systems and Applications
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• v.8 no.3
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• pp.171-178
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• 2013

In this paper, we implement the Faddev-Leverier algorithm using GPGPU (General-Purpose Graphics Processing Unit) to accelerate singular value decomposition. In addition, we compare the performance of the algorithm using CPU and CPU plus GPGPU for eleven ${\times}n$ matrix sizes in order to decompose singular values, where =4, 8, 16, 32, 64, 128, 256, 512, 1,024, 2,048, and 4,096. Experimental results indicate that CPU achieves better performance than CPU plus GPGPU for $n{\leq}64$ because of a large number of read and write operations between CPU and GPGPU. However, CPU plus GPGPU outperforms CPU exponentially in the execution time for $n{\geq}64$.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.997-1002
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• 2001

This paper describes an implementation of inverse filter using SVD in order to recover the input in multi-channel system. The matrix formulation in SISO system is extended to MIMO system. In time and frequency domain we investigates the inversion of minimum phase system and non-minimum phase system. To execute an effective inversion of non-minimum phase system, SVD is introduced. First of all we computes singular values of system matrix and then investigates the phase property of system. In case of overall system is non-minimum phase, system matrix has one (or more) very small singular value(s). The very small singular value(s) carries information about phase properties of system. Using this property, approximate inverse filter of overall system is founded. The numerical simulation shows potentials in use of the inverse filter.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.205-230
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• 2015

A class of periodic type boundary value problems of coupled impulsive fractional differential equations are proposed. Sufficient conditions are given for the existence of solutions of these problems. We allow the nonlinearities p(t)f(t, x, y) and q(t)g(t, x, y) in fractional differential equations to be singular at t = 0, 1 and be involved a sup-multiplicative-like function. So both f and g may be super-linear and sub-linear. The analysis relies on a well known fixed point theorem. An example is given to illustrate the efficiency of the theorems.

• ETRI Journal
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• v.40 no.5
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• pp.634-642
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• 2018

Projection spectral analysis is investigated and refined in this paper, in order to unify principal component analysis and independent component analysis. Singular value decomposition and spectral theorems are applied to nonsymmetric correlation or covariance matrices with multiplicities or singularities, where projections and nilpotents are obtained. Therefore, the suggested approach not only utilizes a sum-product of orthogonal projection operators and real distinct eigenvalues for squared singular values, but also reduces the dimension of correlation or covariance if there are multiple zero eigenvalues. Moreover, incremental learning strategies of projection spectral analysis are also suggested to improve the performance.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.41 no.4
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• pp.29-37
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• 2004

This paper provides a reliable H$_{\infty}$ state feedback controller design method for delayed singular systems with actuator failures occurred within the prescribed subset. The sufficient condition for the existence of a reliable H$_{\infty}$ controller and the controller design method are presented by linear matrix inequality(LMI), singular value decomposition, Schur complements, and changes of variables. The proposed controller guarantees not only asymptotic stability but also H$_{\infty}$ norm bound in spite of existence of actuator failures. Since the obtained sufficient condition can be expressed as an LMI fen all variables can be calculated simultaneously. Moreover, the controller design method can be extended to the problem of robust reliable H$_{\infty}$ controller design method for singular systems with parameter uncertainties, time-varying delay, and actuator failures. A numerical example is given to illustrate the validity of the result.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2011.07a
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• pp.137-140
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• 2011

A precoding strategy is one of the representative interference management techniques in cognitive radio (CR) network which is a typical interference-limited environment. The interference minimization approach to precoding is an appropriate scheme to mitigate the interference efficiently while it may cause the capacity loss of the desired channel. The precoding scheme for the maximal capacity of the desired channel improves the capacity of the desired channel while it increases the interference power and finally causes the capacity loss of the interfered users. Therefore, we propose a precoding scheme which satisfies these two conflicting goals and manages the interference signal in such an interference-limited environment. The proposed scheme consists of two steps. First, the precoder nulls out the largest singular value of the interference channel to mitigate the dominant interference signal based on the interference minimization approach. Second, the transmitter calculates the sum capacities per mode and selects a mode to maximize the sum capacity. In the second step, each mode consists of the right singular vectors corresponding to the singular values except the largest singular value eliminated in the first step. Simulation results show that the proposed precoding scheme not only efficiently mitigate the interference signal, but also has the best performance in terms of the sum capacity in a MIMO-based CR network.

• The Journal of the Acoustical Society of Korea
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• v.28 no.8
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• pp.755-760
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• 2009

In this paper, we apply a reverberation suppression method using difference of singular values to improve the short-distance underwater obstacle detection probability in reverberation environment induced by a linear frequency modulation signal. The reverberation suppression method using difference of singular values suppresses LFM reverberation based on subtracting the singular values for a reference beam, assumed to contain only the reverberation, from those for the current beam of interest, assumed to contain the reverberation and target echo. For the validation, the reverberation suppression method using difference of singular values is applied to real oceanic data, which are acquired using the cross type array.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.6A
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• pp.602-609
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• 2002

In this paper, we propose an robust invisible watermarking method using wavelet transform and singular value decomposition for the ownership protection. of images. For this method, after we decompose the original image in three level using wavelet transform, we use singular value decomposition based key depended watermark insertion method in the lowest band $LL_3.$ And we also watermark using DCT for extraction of watermark and verification of robustness. In the experiments, we found that it had a good quality and robustness in attack such as compression, image processing, geometric transformation and noises. Especially, we know that this method have very high extraction ratio against nose and JPEG compression. And Digimarc's method can not extract watermark in 80 percent compression ratio of JPEG, but the proposed method can extract well.

• Journal of KSNVE
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• v.9 no.1
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• pp.163-173
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• 1999

Precise and reasonable modelling is necessary and indispensable to the analysis of dynamic characteristics of mechanical structures. Also. the effective prediction of the change of modal properties due to the variation of design parameters is required especially for the application of finite element method to the structural dynamics problems. To meet those necessity and requirement, three model updating algorithms are proposed for finite element methods. Those algorithms are based on sensitivity analysis of the modal data obtained from experimental modal analysis(EMA) and analytical modal analysis(AMA). The adapted sensitivity analysis methods of the algorithms are 1)eigensensitivity(EGNS) method. 2)frequency response function sensitivity(FRFS) method. 3)sensitivity based element-by-element method (SBEEM), Singular value decomposition(SVD) is used for performing eigenanalysis and parameter estimation in the updating process. Those algorithms are applied to finite element of a plate and the updating capability of each algorithm is compared in terms of accuracy. reliability and stability of the updating process. It is shown that the model updating method using frequency response function is superior to the other methods in view of various updating capabilities.