• Journal of the Korean Data and Information Science Society
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• 제18권4호
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• pp.1135-1143
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• 2007

The singular value decomposition and the spectral decomposition are the useful methods in the area of matrix computation for multivariate techniques such as principal component analysis and multidimensional scaling. These techniques aim to find a simpler geometric structure for the data points. The singular value decomposition and the spectral decomposition are the methods being used in these techniques for this purpose. In this paper, the singular value decomposition and the spectral decomposition are compared.

• East Asian mathematical journal
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• 제37권3호
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• pp.295-305
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• 2021

In this paper, we analyze the efficiency of a domain decomposition method for the two-dimensional telegraph equations. We formulate the theoretical spectral radius of the iteration matrix generated by the domain decomposition method, because the rate of convergence of an iterative algorithm depends on the spectral radius of the iteration matrix. The theoretical spectral radius is confirmed by the experimental one using MATLAB. Speedup and operation ratio of the domain decomposition method are also compared as the two measurements of the efficiency of the method. Numerical results support the high efficiency of the domain decomposition method.

• 대한수학회지
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• 제59권5호
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• pp.987-996
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• 2022

We introduce the notions of symbolic expansivity and symbolic shadowing for homeomorphisms on non-metrizable compact spaces which are generalizations of expansivity and shadowing, respectively, for metric spaces. The main result is to generalize the Smale's spectral decomposition theorem to symbolically expansive homeomorphisms with symbolic shadowing on non-metrizable compact Hausdorff totally disconnected spaces.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.157-163
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• 2008

Using informations of subsets of divergence points and the relation between members of spectral classes, we give another complete decomposition of spectral classes generated by lower(upper) local dimensions of a self-similar measure on a self-similar Cantor set with full information of their dimensions. We note that it is a complete refinement of the earlier complete decomposition of the spectral classes. Further we study the packing dimension of some uncountable union of distribution sets.

• 충청수학회지
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• 제35권1호
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• pp.91-101
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• 2022

We study some properties of nonwandering set Ω(𝜙) and chain recurrent set CR(𝜙) for an expansive flow which has the POTP on a compact TVS-cone metric spaces. Moreover we shall prove a spectral decomposition theorem for an expansive flow which has the POTP on TVS-cone metric spaces.

• Wind and Structures
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• 제16권5호
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• pp.517-540
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• 2013

This paper presents applications of proper orthogonal decomposition in both the time and frequency domains based on both cross spectral matrix and covariance matrix branches to analyze multi-variate unsteady pressure fields on prisms and to study spanwise and chordwise pressure distribution. Furthermore, modification of proper orthogonal decomposition is applied to a rectangular spanwise coherence matrix in order to investigate the spanwise correlation and coherence of the unsteady pressure fields. The unsteady pressure fields have been directly measured in wind tunnel tests on some typical prisms with slenderness ratios B/D=1, B/D=1 with a splitter plate in the wake, and B/D=5. Significance and contribution of the first covariance mode associated with the first principal coordinates as well as those of the first spectral eigenvalue and associated spectral mode are clarified by synthesis of the unsteady pressure fields and identification of intrinsic events inside the unsteady pressure fields. Spanwise coherence of the unsteady pressure fields has been mapped the first time ever for better understanding of their intrinsic characteristics.

• 대한기계학회논문집B
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• 제22권7호
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• pp.1030-1040
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• 1998

One of the main unresolved issues in large-eddy simulation(LES) of wall-bounded turbulent flows is the requirement of high spatial resolution in the near-wall region, especially in the spanwise direction. Such high resolution required in the near-wall region is generally used throughout the computational domain, making simulations of high Reynolds number, complex-geometry flows prohibitive. A grid-embedding strategy using a nonconforming spectral domain-decomposition method is proposed to address this limitation. This method provides an efficient way of clustering grid points in the near-wall region with spectral accuracy. LES of transitional and turbulent channel flow has been performed to evaluate the proposed grid-embedding technique. The computational domain is divided into three subdomains to resolve the near-wall regions in the spanwise direction. Spectral patching collocation methods are used for the grid-embedding and appropriate conditions are suggested for the interface matching. Results of LES using the grid-embedding strategy are promising compared to LES of global spectral method and direct numerical simulation. Overall, the results show that the spectral domain-decomposition grid-embedding technique provides an efficient method for resolving the near-wall region in LES of complex flows of engineering interest, allowing significant savings in the computational CPU and memory.

• East Asian mathematical journal
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• 제39권1호
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• pp.75-85
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• 2023

In this paper, a non-overlapping rectangular domain decomposition method is presented in order to numerically solve two-dimensional telegraph equations. The method is unconditionally stable and efficient. Spectral radius of the iteration matrix and convergence rate of the method are provided theoretically and confirmed numerically by MATLAB. Numerical experiments of examples are compared with several methods.

• 한국음향학회지
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• 제21권3호
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• pp.315-322
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• 2002

본 논문에서는 음성 신호 시간축 분할의 새로운 기법으로, 비트율과 왜곡을 함께 고려한 기법이 제안되었다. 시간축 분할에 필요한 보간 함수는 학습 음성 데이터로부터 얻어진다. 보간 함수는 두 타겟간의 길이에 따라 유일하게 결정되므로 보간 함수는 추가 정보없이 표현된다. 타겟 샘플은 비트율을 최소화시키면서 동시에 최대 스펙트럼 오차가 문턱 치보다 작게 되도록 선택하였다. 제안된 기법은 음성 부호화기의 스펙트럼 변수로 널리 사용되는 LSP계수의 부호화에 적용되었으며, 모의실험 결과 평균적으로 8 bits/Frame의 비트율에서 1.4 dB의 스펙트럼 왜곡이 얻어짐을 알 수 있었다.

• 전자공학회논문지
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• 제52권2호
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• pp.162-170
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• 2015

컴뮤트 타임 임베딩을 구현하려면 그래프 라플라시안 행렬의 고유값과 고유벡터를 구하여야 하는데, $o(n^3)$의 계산량이 요구되어 대용량 데이터에는 적용하기 어려운 문제가 있다. 이를 줄이기 위하여 표본화 과정을 통하여 크기가 줄어든 그래프 라플라시안 행렬에서 구한 다음, 원래의 고유값과 고유벡터를 근사화시키는 Nystr${\ddot{o}}$m 기법을 주로 채택한다. 이 과정에서 많은 오차가 발생하는데, 이를 개선하기 위하여 본 논문에서는 그래프 라플라시안 대신에 가중치 행렬을 표본화하고 이로부터 구한 고유값과 고유벡터를 그래프 라플라시안의 고유값과 고유벡터로 변환하는 기법을 이용하여 대용량 데이터로 구성된 스펙트럴 그래프를 근사적으로 컴뮤트 타임 임베딩하는 기법을 제안한다. 하지만, 이 방식도 스펙트럼 분해를 계산하여야 하므로 데이터의 크기가 증가하면 적용하기 어려운 문제가 발생한다. 이의 대안으로, 스펙트럼 분해를 계산하지 않고도 데이터 집합의 크기에 영향을 받지 않으면서 컴뮤트 타임을 근사적으로 계산하는 방식을 구현하고 이들의 특성을 실험적으로 분석한다.