• 대한수학회보
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• 제53권1호
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• pp.247-262
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• 2016

We propose and analyze spectral and pseudo-spectral Jacobi-Galerkin approaches for weakly singular Volterra integral equations (VIEs). We provide a rigorous error analysis for spectral and pseudo-spectral Jacobi-Galerkin methods, which show that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

• Structural Engineering and Mechanics
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• 제75권3호
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• pp.311-325
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• 2020

In applying the spectral stochastic finite element methods to the frequency response analysis, the conventional methods are known to give unstable and inaccurate results near the natural frequencies. To address this issue, a new sensitivity based stabilized formulation for stochastic frequency response analysis is proposed in this paper. The main difference over the conventional spectral methods is that the polynomials of random variables are applied to both numerator and denominator in approximating the harmonic response solution. In order to reflect the resonance behavior of the structure, the denominator polynomials is constructed by utilizing the natural frequency sensitivity and the random mode superposition. The numerator is approximated by applying a polynomial chaos expansion, and its coefficients are obtained through the Galerkin or the spectral projection method. Through various numerical studies, it is seen that the proposed method improves accuracy, especially in the vicinities of structural natural frequencies compared to conventional spectral methods.

• 대한수학회지
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• 제44권6호
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• pp.1281-1290
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• 2007

We introduce three spectral regularization methods for solving a backward heat conduction problem (BHCP). For the three spectral regularization methods, we give the stability error estimates with optimal order under an a-priori and an a-posteriori regularization parameter choice rule. Numerical results show that our theoretical results are effective.

• 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.

• 대한수학회지
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• 제50권6호
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• pp.1291-1310
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• 2013

This paper develops least-squares pseudo-spectral collocation methods for elliptic boundary value problems having interface conditions given by discontinuous coefficients and singular source term. From the discontinuities of coefficients and singular source term, we derive the interface conditions and then we impose such interface conditions to solution spaces. We define two types of discrete least-squares functionals summing discontinuous spectral norms of the residual equations over two sub-domains. In this paper, we show that the homogeneous least-squares functionals are equivalent to appropriate product norms and the proposed methods have the spectral convergence. Finally, we present some numerical results to provide evidences for analysis and spectral convergence of the proposed methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권2호
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• pp.31-40
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• 1998

Spectral analysis by energy method is given for a fully discrete methods for hyperbolic integro-differential equations with a weakly singular kernel. Stability and error estimates in $H^1$-norm are derived.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.963-980
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• 2009

In this paper, spectral scheme based on Hermite interpolation for solving partial differential equations is presented. The idea of this Hermite spectral method comes from the spectral method on arbitrary grids of Carpenter and Gottlieb [J. Comput. Phys. 129(1996) 74-86] using the Lagrange interpolation.

• Current Optics and Photonics
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• 제5권5호
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• pp.562-575
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• 2021

As a new type of spectrometer, that based on filters with different transmittance features attracts a lot of attention for its advantages such as small-size, low cost, and simple optical structure. It uses post-processing algorithms to achieve target spectrum reconstruction; therefore, the performance of the spectrometer is severely affected by noise. The influence of noise on the spectral reconstruction results is studied in this paper, and suggestions for solving the spectral reconstruction problem under noisy conditions are given. We first list different spectral reconstruction methods, and through simulations demonstrate that these methods show unsatisfactory performance under noisy conditions. Then we propose to apply the gradient projection for sparse reconstruction (GRSR) algorithm to the spectral reconstruction method. Simulation results show that the proposed method can significantly reduce the influence of noise on the spectral reconstruction process. Meanwhile, the accuracy of the spectral reconstruction results is dramatically improved. Therefore, the practicality of the filter-based spectrometer will be enhanced.

• 자원환경지질
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• 제22권1호
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• pp.81-87
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• 1989

자력탐사 해석에 있어서 Slope, graphical, spectral 및 Fourier 해석 등을 포함한 많은 심도계산 방법들이 연구 발표되었다. 그러나 Peters의 half-slope 및 Vacquier 둥의 maximum-slope 방법들이 석유 탐사에 종사하는 지구물리학자들 간에 인기가 있고 널리 사용되고 있다. Slope 방법은 그 적용이 간단하고 쉬울 뿐만 아니라 대체적으로 신뢰성 있는 결과를 준다. Spectral 방법은 평균 깊이의 추정에는 빠르고 효과적이기는 하지만 고립된 개개 자력이상에 적용될 때 믿을 수 없는 결과가 나온다. Spectral 방법의 문제점을 줄이고 결과의 정확도를 높이기 위해서 이 방법의 신뢰도와 적용한계점에 대한 논의를 제시한다.

• 대한원격탐사학회지
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• 제28권1호
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• pp.39-54
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• 2012

본 연구의 목적은 KOMPSAT-2 위성영상에 가장 일반적으로 적용 가능한 영상융합기법을 제시하는 것이다. 가장 널리 사용되는 영상융합기법인 HPF, modified IHS, pan-sharpened, wavelet을 지역적, 계절적 특성이 서로 다른 4장의 KOMPSAT-2 위성영상에 적용하였고, 각각의 융합결과를 공간적, 분광적으로 비교분석하였다. 영상융합기법의 품질평가는 시각적 분석과 정량적 분석을 병행하여 수행하였으며, 정량적 분석에는 spatial ERGAS, spectral ERGAS, SAM, Q4가 사용되었다. 종합적인 분석결과를 고려할 때, pan-sharpened가 색상정보와 공간정보의 균형적인 보존 측면에서 다른 융합기법들에 비해, 상대적으로 우수한 결과를 나타냈다. modified-IHS의 경우, 공간정보는 잘 보존하였지만 다소 큰 색상 왜곡이 발생되었고, HPF와 wavelet은 색상 왜곡은 적었지만, 공간정보의 왜곡이 발생하였다.