• Journal of applied mathematics & informatics
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• 제28권1_2호
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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.

• 대한임베디드공학회논문지
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• 제8권3호
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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 $n{\geq}64$.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 춘계학술대회논문집
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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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• 제23권1호
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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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• 제40권5호
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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.

• 전자공학회논문지SC
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• 제41권4호
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• pp.29-37
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• 2004

본 논문에서는 구동기 고장을 가지는 시간지연 특이시스템의 신뢰 H/sub ∞/ 상태궤환 제어기 설계방법을 제안한다. 미리 설정한 영역내에서의 구동기 고장이 발생함에도 불구하고 특이시스템의 점근적 안정성(asymptotic stability)과 H/sub ∞/ 성능지수를 만족하는 신뢰 H/sub ∞/ 제어기가 존재할 조건과 제어기 설계 기법을 선형행렬부등식, 특이값 분해(singular value decomposition), 슈어 여수정리(Schur complements), 변수 치환 등에 의하여 제시한다. 제안한 충분조건은 구하려는 모든 변수의 견지에서 하나의 선형행렬부등식으로 표현되기 때문에 모든 해를 동시에 구할 수 있다는 장점이 있다. 또한, 제안한 알고리듬을 이용하면 변수불확실성과 시간지연을 가지는 특이시스템에 대한 강인 신뢰(robust reliable) H/sub ∞/ 제어기 설계문제에도 쉽게 확장됨을 보인다. 마지막으로, 제안한 알고리듬의 타당성을 수치예제를 통하여 확인한다.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2011년도 하계학술대회
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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.

• 한국음향학회지
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• 제28권8호
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• pp.755-760
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• 2009

본 논문에서는 근거리에 위치한 수중 장애물의 탐지 성능을 향상시키기 위해 잔향의 영향을 감소시키는 여러 기법 중 특이 값 차이를 이용한 잔향 감소 기법을 적용한다. 특이 값 차이를 이용한 잔향 감소 기법은 중심 빔 신호에 잔향과 표적이 포함되어 있다고 가정하고 인접한 빔 신호를 참조 신호로 사용하여 중심 빔 신호와의 특이 값 차이를 이용함으로써 잔향 신호를 감소시킨다. 그리고 한국 근해에서 십자형 구조의 송수신 장치를 통해 얻어진 실측 데이터를 이용하여 수중 장애물 탐지에서의 제시한 기법의 타당성을 검증한다.

• 한국통신학회논문지
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• 제27권6A호
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• pp.602-609
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• 2002

본 논문에서는 웨이블릿 변환과 특이치 분해를 이용하여 영상의 소유권 보호론 위한 시각적으로 눈에 띄지 않는 강인한 워터마킹 기법을 제안하고 있다. 이를 위하여, 우선 웨이블릿 변환을 사용하여 level 3에서 원 영상을 분해한 후, 최저주파수 대역에 해당하는 LL$_3$ 대역에 특이치 분해에 기반한 키 종속적인 워터마크를 삽입하는 방법을 사용하고 있다. 또한 워터마크의 검출과 강인성 검증을 위하여 DCT 변환을 이용하여 워터마크의 검출을 하였다. 실험에서 우리는 여러 가지 공격에서도 삽입한 워터마크가 강인함을 알 수 있었다. 특히, 노이즈의 공격과 JPEG 압축의 경우에도 매우 높은 추출률을 보였다. 그리고, Digimarc사의 방법을 통한 추출에서 JPEG 압축의 경우 압축률 80%에서는 삽입된 워터마크를 추출하지 못함을 알 수 있었으나 본 논문의 알고리즘에서는 80%의 압축에서도 삽입된 워터마크가 잘 추출됨을 볼 수 있었다.

• 소음진동
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• 제9권1호
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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.