• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2003년도 춘계학술대회 논문집
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• pp.21-26
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• 2003

The well-conditioned observer in a stochastic system is designed so that the observer is less sensitive to the ill-conditioning factors in transient and steady-state observer performance. These factors include not only deterministic issues such as unknown initial estimation error, round-off error, modeling error and sensing bias, but also stochastic issues such as disturbance and sensor noise. In deterministic perspectives, a small value in the L$_2$ norm condition number of the observer eigenvector matrix guarantees robust estimation performance to the deterministic issues and its upper bound can be minimized by reducing the observer gain and increasing the decay rate. Both deterministic and stochastic issues are considered as a weighted sum with a LMI (Linear Matrix Inequality) formulation. The gain in the well-conditioned observer is optimally chosen by the optimization technique. Simulation examples are given to evaluate the estimation performance of the proposed observer.

• 대한수학회보
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• 제39권1호
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• pp.9-22
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• 2002

We consider the hp-version to solve non-constant coefficient elliptic equations with Dirichlet boundary conditions on a bounded, convex polygonal domain $\Omega$ in $R^{2}.$ To compute the integrals in the variational formulation of the discrete problem we need the numerical quadrature rule scheme. In this paler we consider a family $G_{p}= {I_{m}}$ of numerical quadrature rules satisfying certain properties. When the numerical quadrature rules $I_{m}{\in}G_{p}$ are used for calculating the integrals in the stiffness matrix of the variational form we will give its variational fore and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_0,{\Omega}'$.

• 대한수학회보
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• 제47권6호
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• pp.1225-1234
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• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• Current Optics and Photonics
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• 제5권3호
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• pp.270-277
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• 2021

The adaptive sparse representation (ASR) can effectively combine the structure information of a sample dictionary and the sparsity of coding coefficients. This algorithm can effectively consider the correlation between training samples and convert between sparse representation-based classifier (SRC) and collaborative representation classification (CRC) under different training samples. Unlike SRC and CRC which use fixed norm constraints, ASR can adaptively adjust the constraints based on the correlation between different training samples, seeking a balance between l₁ and l₂ norm, greatly strengthening the robustness and adaptability of the classification algorithm. The correlation coefficients (CC) can better identify the pixels with strong correlation. Therefore, this article proposes a hyperspectral image classification method called correlation coefficients and adaptive sparse representation (CCASR), based on ASR and CC. This method is divided into three steps. In the first step, we determine the pixel to be measured and calculate the CC value between the pixel to be tested and various training samples. Then we represent the pixel using ASR and calculate the reconstruction error corresponding to each category. Finally, the target pixels are classified according to the reconstruction error and the CC value. In this article, a new hyperspectral image classification method is proposed by fusing CC and ASR. The method in this paper is verified through two sets of experimental data. In the hyperspectral image (Indian Pines), the overall accuracy of CCASR has reached 0.9596. In the hyperspectral images taken by HIS-300, the classification results show that the classification accuracy of the proposed method achieves 0.9354, which is better than other commonly used methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권3호
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• pp.211-236
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• 2019

This paper is devoted to the study and investigation of the Runge-Kutta discontinuous Galerkin method for a system of differential equations consisting of two hyperbolic conservation laws. The numerical coupling flux which is used at a given interface (x = 0) is the upwind flux. Moreover, in the linear case, we derive optimal convergence rates in the $L_2$-norm, showing an error estimate of order ${\mathcal{O}}(h^{k+1})$ in domains where the exact solution is smooth; here h is the mesh width and k is the degree of the (orthogonal Legendre) polynomial functions spanning the finite element subspace. The underlying temporal discretization scheme in time is the third-order total variation diminishing Runge-Kutta scheme. We justify the advantages of the Runge-Kutta discontinuous Galerkin method in a series of numerical examples.

• 전자공학회논문지SC
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• 제39권5호
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• pp.26-33
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• 2002

본 논문에서는 볼록 한계 불확실성(convex bounded uncertainty)을 가지는 이산시간 선형 시스템의 견실 $H_{\infty}$ 필터 설계 알고리듬을 제안한다. 다루고 있는 파라미터 불확실성은 폴리토프형(polytope type) 볼록 한계를 가지는 형태이다. 본 논문의 목적은 필터링 오차 시스템의 점근 안정성(asymptotic stability)과 변형한 성능지수의 유도 $L_2$ 노옴($L_2$ induced norm) 한계치를 해적적으로 제시하는 안정한 견실 $H_{\infty}$ 필터를 설계하는 것이다. 견실 $H_{\infty}$ 필터가 존재할 충분조건과 필터 설계 방법은 볼록 최적화 기법에 의하여 효과적으로 해를 구하는 선형행렬부등식 방법에 의하여 제시한다. 제안한 알고리듬의 타당성은 예제를 통하여 확인한다.

• 대한기계학회논문집A
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• 제28권5호
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• pp.503-510
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• 2004

In this paper, the well-conditioned observer for a stochastic system is designed so that the observer is less sensitive to the ill-conditioning factors in transient and steady-state observer performance. These factors include not only deterministic uncertainties such as unknown initial estimation error, round-off error, modeling error and sensing bias, but also stochastic uncertainties such as disturbance and sensor noise. In deterministic perspectives, a small value in the L$_{2}$ norm condition number of the observer eigenvector matrix guarantees robust estimation performance to the deterministic uncertainties. In stochastic viewpoints, the estimation variance represents the robustness to the stochastic uncertainties and its upper bound can be minimized by reducing the observer gain and increasing the decay rate. Both deterministic and stochastic issues are considered as a weighted sum with a LMI (Linear Matrix Inequality) formulation. The gain in the well-conditioned observer is optimally chosen by the optimization technique. Simulation examples are given to evaluate the estimation performance of the proposed observer.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권2호
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• pp.125-140
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• 2010

This paper develops a least-squares approach to the solution of the optimal control problem for the Navier-Stokes equations. We recast the optimality system as a first-order system by introducing velocity-flux variables and associated curl and trace equations. We show that a least-squares principle based on $L^2$ norms applied to this system yields optimal discretization error estimates in the $H^1$ norm in each variable.

• 충청수학회지
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• 제29권2호
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• pp.267-281
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• 2016

In this paper, we consider multi-degree reduction of $B{\acute{e}}zier$ curves with continuity of any (r, s) order with respect to $L_2$ norm. With help of matrix theory about generalized inverses we can use Lagrange multipliers to obtain the degree reduction matrix in a very simple form as well as the degree reduced control points. Also error analysis comparing with the least squares degree reduction without constraints is given. The advantage of our method is that the relationship between the optimal multi-degree reductions with and without constraints of continuity can be derived explicitly.

• 한국정보통신학회논문지
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• 제4권5호
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• pp.963-969
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• 2000

본 논문에서는, 선형 주기적 시변 시스템에 대해서, 두 개의 입출력 이득을 정의한다. 그 하나는 단위 크기의 ι$_2$노름을 갖는 모든 입력에 대한 최악의 $\iota_2$ 노름의 출력의 비로서, G($\iota_2,\iota_2$ 로 표기한다. 또 다른 하나는 단위 크기의 RMS 값을 갖는 모든 입력에 대한 최악의 RMS 값의 출력의 비로서, G(RMS, RMS)로 표기한다. 선형 시불변 시스템에 대해서는 이 두 개의 이득은 등가라는 사실이 잘 알려져 있다. 본 논문에서는 선형 주기적 시변 시스템에 대해서도 이 두 개의 이득이 등가라는 것을 증명한다. 또한, 선형 주기적 시변 시스템에 대한 주파수 응답을 얻는 두 가지 방법 사이의 관계를 유도한다. 이렇게 정의된 입출력 이득은 M-채널 필터 뱅크에 적용한다. 필터 뱅크는 음성 압축 등에 사용되는 대표적인 다중비 신호처리 시스템이다. 이러한 필터뱅크에는 일반적으로 에일리어징 왜곡, 진폭 왜곡 및 위상 왜곡이 존재한다. 본 논문에서는 오차 시스템의 G($\iota_2,\iota_2$ 이득을 최적화 하는 방법에 의해 필터 뱅크를 설계함으로써, 필터 뱅크에서 일반적으로 존재하는 왜곡을 작게할 수 있음을 보인다.