• Proceedings of the KSME Conference
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• 2000.04a
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• pp.339-344
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• 2000

Newton-Raphson 기법은 구조물의 비선형 해석에 널리 쓰이는 반복계산기법이다. 비선형 해석을 위한 반복계산기법은 컴퓨터의 발달을 감안해도 상당한 계산시간이 소요된다. 본 논문에서는 신경회로망 예측을 사용한 Predicted Newton-Raphson 반복계산기법을 제안하였다. 통상적인 Newton-Raphson 기법은 이전스텝에서 수렴된 점으로부터 현재 스텝의 반복계산을 시작하는 반면 제시된 방법은 현재 스텝 수렴해에 대한 예측점에서 반복계산을 시작한다. 수렴해에 대한 예측은 신경회로망을 사용하여 이전 스텝 수렴해의 과거경향을 파악한 후 구한다. 반복계산 시작점이 수렴점에 보다 근접하여 위치하므로 수렴속도가 빨라지게 되고 허용되는 하중스텝의 크기가 커지게 된다. 또한 반복계산의 시작점으로부터 이루어지는 계산과정은 통상적인 Newton-Raphson 기법과 동일하므로 기존의 Newton-Raphson 기법과 정확히 일치하는 수렴해를 구할 수 있다. 구조물의 정적 비선형 거동에 대한 수치해석을 통하여 modified Newton-Raphson 기법과 제시된 Predicted Newton=Raphson 기법의 정확성과 효율성을 비교하였다. 제시된 Predicted Newton-Raphson 기법은 modified Newton-Raphson 기법과 동일한 해를 산출하면서도 계산상의 효율성이 매우 큼을 확인할 수 있었다.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.38 no.4
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• pp.11-19
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• 2001

In this paper, we study the convergence property of iterative learning control (ILC). First, we present a new method to prove the convergence of ILC using sup-norm. Then, we propose a new type of ILC algorithm adopting intervalized learning scheme and show that the monotone convergence of the output error can be obtained for a given time interval when the proposed ILC algorithm is applied to a class of linear dynamic systems. We also show that the divided time interval is affected from the learning gain and that convergence speed of the proposed learning scheme can be increased by choosing the appropriate learning gain. To show the effectiveness of the proposed algorithm, two numerical examples are given.

• Journal of Korean Society of Steel Construction
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• v.10 no.3 s.36
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• pp.473-486
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• 1998

A numerically stable technique to remove the limitation in choosing a shift in the subspace iteration method with shift is presented. A major difficulty of the subspace iteration method with shift is that because of singularity problem, a shift close to an eigenvalue can not be used, resulting in slower convergence. This study solves the above singularity problem using side conditions without sacrifice of convergence. The method is always nonsingular even if a shift is an eigenvalue itself. This is one of the significant characteristics of the proposed method. The nonsingularity is proved analytically. The convergence of the proposed method is at least equal to that of the subspace iteration method with shift, and the operation counts of above two methods are almost the same when a large number of eigenpairs are required. To show the effectiveness of the proposed method, two numerical examples are considered.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.3
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• pp.371-383
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• 1999

An efficient and numerically stable eigensolution method for structures with multiple natural frequencies is presented. The proposed method is developed by improving the well-known subspace iteration method with shift. A major difficulty of the subspace iteration method with shift is that because of singularity problem, a shift close to an eigenvalue can not be used, resulting in slower convergence. In this paper, the above singularity problem has been solved by introducing side conditions without sacrifice of convergence. The proposed method is always nonsingular even if a shift is on a distinct eigenvalue or multiple ones. This is one of the significant characteristics of the proposed method. The nonsingularity is proved analytically. The convergence of the proposed method is at least equal to that of the subspace iteration method with shift, and the operation counts of above two methods are almost the same when a large number of eigenpairs are required. To show the effectiveness of the proposed method, two numerical examples are considered.

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.2
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• pp.175-179
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• 2003

Convergence condition determines performance of iterative learning control (ILC), for example, convergence speed, remaining error, etc. Hence, the performance can be elevated and a feasible set of learning controllers grows if a less conservative condition is obtained. In the frequency domain, the $H_{\infty}$ norm of the transfer function between consecutive errors has been currently used to test convergence of a learning system. However, even if the convergence condition based on the $H_{\infty}$ norm has a clear property about monotonic convergence, it has a few drawbacks, especially in MIMO plants. In this paper, the relation between the condition and the monotonicity of convergence is clarified and a modified convergence condition is found out using a frequency domain Lyapunov equation, which supersedes the conventional one in the frequency domain.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1996.06a
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• pp.237-240
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• 1996

본 논문에서는 방향성을 갖는 새로운 공간적응 조절연산자와 비선형필터를 이용한 제한 반복적 영상복원 알고리듬을 제안하고 제안한 알고리듬의 수렴성에 대하여 분석을 하고 있다. 일반적인 제한반복적 영상복원 기법에서는 열화된 영상을 복원하는 과정에서 에지 및 경계부분의 재번짐이 지나친 잡음성분의 증폭에 의한 고리현상 등이 발생한다. 이러한 문제들을 해결하기 위하여 본 논문에서는 다음과 같은 기법을 도입하고 있다. 첫째는, 방향성을 갖는 새로운 공간적응 조절연산자를 적용하여 에지 등의 재번짐을 막고 고주파수 영역의 복원성능을 개선하고 있다. 둘째로, 적응적인 비선형필터를 사용하여 잡음성분과 같은 고주파수 영역의 지나친 증폭에 따른 문제를 해결하고 있다. 그리고, 제안한 논문의 안정성과 수렴성을 보장하기 위한 조건을 분석하고 있다. 열화된 영상에 대하여 실험한 결과, 기존의 다른 결과보다 우수한 성능이 있었고, 특히, 에지의 복원성능 및 고리현상의 제거에 두드러진 특징을 나타내었다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.8
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• pp.891-897
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• 1992

A local iterative Image restoration method Is Introduced that processes with varying iteration numbers according to the local statistics. In general almost of the Iterative method applies Its algorithm to the whole Image without considering the local pixel informations, which Is not so effective for the processing time. Usually the edges or details have an Important role In visual effect. So in this paper we process the edges or the details many times while In the flat region we just pass over or decrease iterations. This method shows good MSE (Mean Square Error) improvement, better subjective qualify and reduced processing time.

• Computational Structural Engineering
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• v.11 no.1
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• pp.205-216
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• 1998

A solution method is presented to solve the eigenvalue problem arising in the dynamic analysis of nonclassicary damped structural systems with multiple eigenvalues. The proposed method is obtained by applying the modified Newton-Raphson technique and the orthonormal condition of the eigenvectors to the linear eigenproblem through matrix augmentation of the quadratic eigenvalue problem. In the iteration methods such as the inverse iteration method and the subspace iteration method, singularity may be occurred during the factorizing process when the shift value is close to an eigenvalue of the system. However, even though the shift value is an eigenvalue of the system, the proposed method provides nonsingularity, and that is analytically proved. Since the modified Newton-Raphson technique is adopted to the proposed method, initial values are need. Because the Lanczos method effectively produces better initial values than other methods, the results of the Lanczos method are taken as the initial values of the proposed method. Two numerical examples are presented to demonstrate the effectiveness of the proposed method and the results are compared with those of the well-known subspace iteration method and the Lanczos method.

• The KIPS Transactions:PartA
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• v.11A no.2
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• pp.203-206
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• 2004

Wegmann's method has been known as the most efficient one for the Theodorsen equation that is needed to solve conformal mapping. It was researched in the earlier studies (1). However divergence was revealed in some difficult problems by numerical experiment using Wegmann's method. We analyzed the cause of divergence and proposed an improved method by applying a low frequency pass filter to Wegmann's method. Numerical experiments using the improved method showed convergence for all divergent problems using the Wegmann's method. In this paper, we prove theroretically the cause of convergence in the Numerical experiment using the improved method by applying a low frequency pass filter to Wegmann's method. We make use of Fourier transforms in this theoretical proof of convergence.

• Proceedings of the Korea Information Processing Society Conference
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• 2002.11a
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• pp.419-422
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• 2002

저자는 등각사상을 추하기 위한 기존의 여러 Theodorsen 방정식의 해법 중 가장 유효한 해법으로 알려져 있는 Wegmann의 방법을 다룬바 있다. Wegmann의 방법으로 수치실험을 한 결과 난이도가 높다고 예상되는 문제에 있어 수렴했다가 발산을 하는 불안정현상이 나타났으며 수렴하지 않는 불안정현상의 원인을 분석하여 저주파필터를 적용한 새로운 반복법을 제안하여 Wegmann 방법으로는 발산하는 모든 문제에 있어서 수렴하는 수치실험 결과를 얻었다[1]. 본 논문에서는 저주파필터를 적용한 해법에 의해 수치적으로 수렴한 결과를 이론적으로 증명한다.