• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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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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• v.75 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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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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• v.18 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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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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• v.2 no.2
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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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• v.27 no.3_4
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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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• v.5 no.5
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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.

• Economic and Environmental Geology
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• v.22 no.1
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• pp.81-87
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• 1989

Many depth estimation techniques for magnetic exploration, such as the slope methods, graphica1 methods, spectral analysis, and Fourier ana1ysis have been published. Nevertheless, it appears that the half-slope method of Peters(1949)and the maximum-slop method of Vacquier et. al. (1951)are more popular and widely used by geophysicists in the hydrocarbon exploration industry. The slope methods are not only simpler and easier to use but are also genera1ly reliable. The spectral method is fast, effective, and powerful in the determination of an average depth. The often unreliable results produced from spectral techniques are attributed to their application to isolated magnetic anomaly cases. The reliability and limitations associated with the method are given in order to minimize problems and increase accuracy in the application of the method.

• Korean Journal of Remote Sensing
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• v.28 no.1
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• pp.39-54
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• 2012

The objective of this study is to propose efficient data fusion techniques feasible to the KOMPSAT-2 satellite images. The most widely used image fusion techniques, which are the high-pass filter (HPF), the intensity-hue-saturation-based (modified IHS), the pan-sharpened, and the wavelet-based methods, was applied to four KOMPSAT - 2 satellite images having different regional and seasonal characteristics. Each fusion result was compared and analyzed in spatial and spectral features, respectively. Quality evaluation of image fusion techniques was performed in both quantitative and visual analysis. The quantitative analysis methods used for this study were the relative global dimensional error (spatial and spectral ERGAS), the spectral angle mapper index (SAM), and the image quality index (Q4). The results of quantitative and visual analysis indicate that the pan-sharpened method among the fusion methods used for this study relatively has the suitable balance between spectral and spatial information. In the case of the modified IHS method, the spatial information is well preserved, while the spectral information is distorted. And also the HPF and wavelet methods do not preserve the spectral information but the spatial information.