• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권3호
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• pp.138-155
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• 2022

To solve the initial value problem we present a new single-step implicit method based on the Euler method. We prove that the proposed method has convergence order 2. In practice, numerical results of the proposed method for some selected examples show an error tendency similar to the second-order Taylor method. It can also be found that this method is useful for stiff initial value problems, even when a small number of nodes are used. In addition, we extend the proposed method by using weighted averages with a parameter and show that its convergence order becomes 2 for the parameter near $\frac{1}{2}$. Moreover, it can be seen that the extended method with properly selected values of the parameter improves the approximation error more significantly.

• 한국융합학회논문지
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• 제13권4호
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• pp.17-24
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• 2022

비트코인은 정부나 금융기관에 의존되어 있지 않은 전자 거래를 지향하며 만들어진 peer-to-peer 방식의 암호화폐이다. 비트코인은 최초 발행 이후 거대한 블록체인 금융 시장을 생성했고, 이에 따라 기계 학습을 이용한 비트코인 가격 데이터를 예측하는 연구들이 활발해졌다. 그러나 기계 학습 연구의 비효율적인 Hyper-parameter 최적화 과정이 연구 진행에 있어 비용적인 측면을 악화시키고 있다. 본 논문은 LSTM(Long Short-Term Memory) 층을 사용하는 비트코인 가격 예측 모델에서 가장 대표적인 Hyper-parameter 중 Timesteps, LSTM 유닛의 수, 그리고 Dropout 비율의 전체 조합을 구성하고 각각의 조합에 대한 예측 성능을 측정하는 실험을 통해 정확한 비트코인 가격 예측을 위한 Hyper-parameter 최적화의 방향성을 분석하고 제시한다.

• 대한전자공학회논문지
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• 제19권5호
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• pp.12-19
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• 1982

현재까지의 적응 필터(adaptive filter)의 설계 방법을 대별하면 국부 파라미타 최적화(local parameter optimization)방법[1]과 안정성(stability)을 주한점으로 하는 방법[1-3] 의 두 가지로 된다. 그리고 이들 중에서 비교적 간단한 방법은 로칼 파라미터 최적화 방법으로서, 이것에서는 스티피스트-디샌트(steepest-descent)방법[15]을 이용하는 LMS 알고리즘을 대표적인 것으로 들 수 있다. 적응 필터의 설계에 있어서 가장 중요한 것은 수검 속도를 높이는 일이다. 본 논문은 적응 비순환 필터의 설계를 위한 고속 수검 알고리즘을 개발하는 문제에 관하여 연구한 것으로, 적응 이득(adaptation-gain)을 적절히 조정함으로써, 종래 사용되어 오던 LMS 알고리즘 및 그의 변형인 여러 알고리즘에 비하여 수검 속도를 높일 수 있으며 동시에 안정성이 높은 새로운 알고리즘을 제시하였다. 그리고 제안된 알고리즘을 이용한 적응 필터의 특성 배선 문제를 다각도로 검토하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권2호
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• pp.1-4
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• 1999

The Helmholtz equation is very important in physics and engineering. However, solution of the Helmholtz equation is in general known as a very difficult phenomenon. For if the ${\omega}$ is negative, the FDM discretized linear system becomes indefinite, whose solution by iterative method requires a very clever preconditioner. In this paper we assume that ${\omega}$ is nonnegative, and determine the optimal ${\rho}$ parameter for the three dimensional ADI iteration for the Helmholtz equation. The ADI(Alternating Direction Implicit) method is also getting new attentions due to the fact that it is very suitable to the vector/parallel computers, for example, as a preconditioner to the Krylov subspace methods. However, classical ADI was developed for two dimensions, and for three dimensions it is known that its convergence behaviour is quite different from that in two dimensions. So far, in three dimensions the so-called Douglas-Rachford form of ADI was developed. It is known to converge for a relatively wide range of ${\rho}$ values but its convergence is very slow. In this paper we determine the necessary conditions of the ${\rho}$ parameter for the convergence and optimal ${\rho}$ for the three dimensional ADI iteration of the Peaceman-Rachford form for the real Helmholtz equation with nonnegative ${\omega}$. Also, we conducted some experiments which is in close agreement with our theory. This straightforward extension of Peaceman-rachford ADI into three dimensions will be useful as an iterative solver itself or as a preconditioner to the the Krylov subspace methods, such as CG(Conjugate Gradient) method or GMRES(m).

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.419-435
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• 2021

This paper deals with numerical treatment of singularly perturbed differential equations involving small delays. The highest order derivative in the equation is multiplied by a perturbation parameter 𝜀 taking arbitrary values in the interval (0, 1]. For small 𝜀, the problem involves a boundary layer of width O(𝜀), where the solution changes by a finite value, while its derivative grows unboundedly as 𝜀 tends to zero. The considered problem contains delay on the convection and reaction terms. The terms with the delays are approximated using Taylor series approximations resulting to asymptotically equivalent singularly perturbed BVPs. Inducing exponential fitting factor for the term containing the singular perturbation parameter and using central finite difference for the derivative terms, numerical scheme is developed. The stability and uniform convergence of difference schemes are studied. Using a priori estimates we show the convergence of the scheme in maximum norm. The scheme converges with second order of convergence for the case 𝜀 = O(N^-1) and for the case 𝜀 ≪ N^-1, the scheme converge uniformly with first order of convergence, where N is number of mesh intervals in the domain discretization. We compare the accuracy of the developed scheme with the results in the literature. It is found that the proposed scheme gives accurate result than the one in the literatures.

• 전자공학회논문지B
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• 제33B권6호
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• pp.45-53
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• 1996

In this paper, the convergence behavior of timing phase when an adaptive partial response equalizer and decision-directed type of a PLL work together in a digital recording channel is described. The phenomena of getting biased in timing phase when the convergence parameter of an adaptive partial response equalizer and timing recovery constant of a PLL are not selected properly is introduced. The phenomena, occurring due to perturbation of timing phase, are analyzed, by computer simulation and the region of ocnvergence for timing phase is discussed. Also, a method to overcome the phenomena using a variable step-size parameter is described.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1991년도 하계학술대회 논문집
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• pp.691-694
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• 1991

In a discrete parameter estimation system, the standard least squares method shows slow convergence. On the other hand, the weighted least squares method has relatively fast convergence. However, if the input is not sufficiently rich, then gain matrix grows unboundedly. In order to solve these problems, this paper proposes a modified least squares algorithm which prevents gain matrix from growing unboundedly and has fast convergence.

• 한국소음진동공학회논문집
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• 제11권9호
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• pp.462-474
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• 2001

In this paper, Generalized Differential Quadrature Method is applied to the buckling analysis of built-up columns without or with stay plates. numerical analysis using GDQM is carried out for various boundary conditions(simply supported conditions, fixed conditions, fixed-simply supported conditions), dimensionless stiffness parameter and dimensionless inertia moment parameter. The accuracy and convergence of solutions are compared with exact solutions of Gjelsvik to validate the results of GDQM. Results obtained by this method are as follows. 91) This method can yield the accurate numerical solutions using few grid points. (2) The buckling load of built-up column increases as the dimensionless stiffness parameter decreases. (3) The effects of boundary conditions on the buckling load are not considerable as the dimensionless stiffness parameter increases. (4) The buckling load of built-up column increases due to the stay plate.

• 한국산업융합학회 논문집
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• 제10권3호
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• pp.143-147
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• 2007

In recents years, the statistical properties has become an important quantity for reliability based design of a component. The effects of the materials and test conditions for parameter estimation in residual strength degradation model are studied in carbon/epoxy laminate. It is shown that the correlation between the experimental results and the theoretical prediction on the fatigue life distribution using the life distribution convergence method is very reasonable.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1986년도 한국자동제어학술회의논문집; 한국과학기술대학, 충남; 17-18 Oct. 1986
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• pp.83-85
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• 1986

The error differential equations which are derived by using the first error model are uniformly asymptotial stable if the input is bounded and sufficiently rich. In the adaptive control, the speed of convergence of system output or parameter error in such cases is of both practical and theoretical interest. In this paper, the adaptive algorithms(Gradient algorithm, Intergral algorithm) are discussed from the point of view of speed convergence and the modification of adaptive law for prohibition of overadaptation is discussed. The result is compared among this algorithms and the adaptive gain is choosed by this result(the speed of convergence).