• East Asian mathematical journal
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• v.37 no.3
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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.

• East Asian mathematical journal
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• v.39 no.1
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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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.7
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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.

• The Journal of the Acoustical Society of Korea
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• v.21 no.3
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• pp.315-322
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• 2002

In this paper, a new temporal decomposition method is proposed. which takes into consideration not only spectral distortion but also bit rates. The interpolation functions, which are one of necessary parameters for temporal decomposition, are obtained from the training speech corpus. Since the interval between the two targets uniquely defines the interpolation function, the interpolation can be represented without additional information. The locations of the targets are determined by minimizing the bit rates while the maximum spectral distortion maintains below a given threshold. The proposed method has been applied to compressing the LSP coefficients which are widely used as a spectral parameter. The results of the simulation show that an average spectral distortion of about 1.4 dB can be achieved at an average bit rate of about 8 bits/Frame.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.33.5-33
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• 2001

We consider here the problem of spectral estimation of multidimensional wide sense stationary (WSS) random process. A method, employing a special difference equation of correlation function, is proposed to solve the problem of multidimensional spectral estimation. In this approach, the special difference equation of correlation function is derived by modal decomposition method. Maximum likelihood estimator and Kalman filter are used to estimate the model parameters of the difference equation and the decomposed spectral residues. An algorithm is presented to estimate the multidimensional spectral density. According to the result of the simulation, these methods are feasible to estimate the spectral density of WSS process, which is realized by finite dimensional multivariable lineal system driven by white noise.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.2
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• pp.162-170
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• 2015

Commute time embedding involves computing the spectral decomposition of the graph Laplacian. It requires the computational burden proportional to $o(n^3)$, not suitable for large scale dataset. Many methods have been proposed to accelerate the computational time, which usually employ the Nystr${\ddot{o}}$m methods to approximate the spectral decomposition of the reduced graph Laplacian. They suffer from the lost of information by dint of sampling process. This paper proposes to reduce the errors by approximating the spectral decomposition of the graph Laplacian using that of the affinity matrix. However, this can not be applied as the data size increases, because it also requires spectral decomposition. Another method called approximate commute time embedding is implemented, which does not require spectral decomposition. The performance of the proposed algorithms is analyzed by computing the commute time on the patch graph.

• Structural Engineering and Mechanics
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• v.17 no.3_4
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• pp.445-466
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• 2004

In this paper, several modal identification techniques for output-only structural systems are extensively investigated. The methods considered are the power spectral method, the frequency domain decomposition method, the Ibrahim time domain method, the eigensystem realization algorithm, and the stochastic subspace identification method. Generally, the power spectral method is most widely used in practical area, however, the other methods may give better estimates particularly for the cases with closed modes and/or with large measurement noise. Example analyses were carried out on typical structural systems under three different loading cases, and the identification performances were examined throught the comparisons between the estimates by various methods.

• Journal of Radiation Protection and Research
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• v.42 no.2
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• pp.91-97
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• 2017

Background: A gamma energy identifying algorithm using spectral decomposition combined with smoothing method was suggested to confirm the existence of the artificial radio isotopes. The algorithm is composed by original pattern recognition method and smoothing method to enhance the performance to identify gamma energy of radiation sensors that have low energy resolution. Materials and Methods: The gamma energy identifying algorithm for the compact radiation sensor is a three-step of refinement process. Firstly, the magnitude set is calculated by the original spectral decomposition. Secondly, the magnitude of modeling error in the magnitude set is reduced by the smoothing method. Thirdly, the expected gamma energy is finally decided based on the enhanced magnitude set as a result of the spectral decomposition with the smoothing method. The algorithm was optimized for the designed radiation sensor composed of a CsI (Tl) scintillator and a silicon pin diode. Results and Discussion: The two performance parameters used to estimate the algorithm are the accuracy of expected gamma energy and the number of repeated calculations. The original gamma energy was accurately identified with the single energy of gamma radiation by adapting this modeling error reduction method. Also the average error decreased by half with the multi energies of gamma radiation in comparison to the original spectral decomposition. In addition, the number of repeated calculations also decreased by half even in low fluence conditions under $10^4$ ($/0.09cm^2$ of the scintillator surface). Conclusion: Through the development of this algorithm, we have confirmed the possibility of developing a product that can identify artificial radionuclides nearby using inexpensive radiation sensors that are easy to use by the public. Therefore, it can contribute to reduce the anxiety of the public exposure by determining the presence of artificial radionuclides in the vicinity.

• Journal of Biomedical Engineering Research
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• v.8 no.1
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• pp.69-74
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• 1987

The power spectrum of background EEG is estimated by the Plsarenko Harmonic Decomposition with the stochastic process whlch consists of the nonhamonic sinus Bid and the white nosie. The estimation results are examined and compared with the results from the maximum entropy spectral extimation, and the optimal order of this from the maximum entropy spectral extimation, and the optimal order of this model can be determined from the eigen value's fluctuation of autocorrelation of background EEG. From the comparing results, this method is possible to estimate the power spectrum of background EEG.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.249-258
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• 1993

It is well known that design matrix X for any factorial design can be represented by a product $X = TX_o$ where T is replication matrix and $X_o$ is the corresponding balanced design matrix. Since $X_o$ consists of regular arrangement of 0's and 1's, we can easily find the spectral decomposition of $X_o',X_o$. Also using this we propose an efficient algorithm for computing the orthogonal projection matrix for a balanced factorial design.