• 대한수학회보
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• 제48권2호
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• pp.303-314
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• 2011

For Ax = b, it has recently been reported that the convergence of the preconditioned Gauss-Seidel iterative method which uses a matrix of the type P = I + S (${\alpha}$) to perform certain elementary row operations on is faster than the basic Gauss-Seidel method. In this paper, we discuss the adaptive Gauss-Seidel iterative method which uses P = I + S (${\alpha}$) + $\bar{K}({\beta})$ as a preconditioner. We present some comparison theorems, which show the rate of convergence of the new method is faster than the basic method and the method in [7] theoretically. Numerical examples show the effectiveness of our algorithm.

• 대한산업공학회지
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• 제17권2호
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• pp.131-142
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• 1991

The concept of criterion function is proposed as a framework for comparing the geometric and computational characteristics of various nonlinear programming approaches to linear programming such as the method of centers, Karmakar's algorithm and the gravitational method. Also, we discuss various computational issues involved in obtaining an efficient parallel implementation of these methods. Clearly, the most time consuming part in solving a linear programming problem is the direction finding procedure, where we obtain an improving direction. In most cases, finding an improving direction is equivalent to solving a simple optimization problem defined at the current feasible solution. Again, this simple optimization problem can be seen as a least squares problem, and the computational effort in solving the least squares problem is, in fact, same as the effort as in solving a system of linear equations. Hence, getting a solution to a system of linear equations fast is very important in solving a linear programming problem efficiently. For solving system of linear equations on parallel computing machines, an iterative method seems more adequate than direct methods. Therefore, we propose one possible strategy for getting an efficient parallel implementation of an iterative method for solving a system of equations and present the summary of computational experiment performed on transputer based parallel computing board installed on IBM PC.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2002년도 ITC-CSCC -3
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• pp.1483-1486
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• 2002

In this paper, a new scheme of iterative loaming control of a robot manipulator is presented. The proposed method uses a fuzzy sliding mode controller(FSMC), which is designed based on the similarity between the fuzzy logic control(FLC) and the sliding mode control(SMC), for the feedback. With this, the proposed method makes possible fDr fast iteration and has advantages that no linear approximation is used for the derivation of the learning law or in the stability proof Full proof of the convergence of the fuzzy sliding base learning scheme Is given.

• International Journal of Aeronautical and Space Sciences
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• 제9권2호
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• pp.79-86
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• 2008

High performance direct-iterative hybrid linear solver for large scale finite element problem is developed. Direct solution method is robust but difficult to parallelize, whereas iterative solution method is opposite for direct method. Therefore, combining two solution methods is desired to get both high performance parallel efficiency and numerical robustness for large scale structural analysis problems. Hybrid method mentioned in this paper is based on FETI-DP (Finite Element Tearing and Interconnecting-Dual Primal method) which has good parallel scalability and efficiency. It is suitable for fourth and second order finite element elliptic problems including structural analysis problems. We are using the hybrid concept of theses two solution method categories, combining the multifrontal solver into FETI-DP based iterative solver. Hybrid solver is implemented for our general structural analysis code, IPSAP.

• Coupled systems mechanics
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• 제7권6호
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• pp.755-774
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• 2018

The Ritz method is known as very successful strategy for discretizing continuous problems, but it has never been used for solving systems of algebraic equations. The Iterated Ritz Method (IRM) is a novel iterative solver based on the discretized Ritz procedure applied at each iteration step. With an appropriate choice of coordinate vectors, the method may be efficient in linear, nonlinear and optimization problems. Additionally, some iterative methods can be explained as special cases of this approach, which helps to understand advantages and limitations of these methods and gives motivation for their improvement in sense of IRM. In this paper, some ideas for generation of efficient coordinate vectors are presented. The algorithm was developed and tested independently and then implemented into the open source program FEAP. Method has been successfully applied to displacement based (even ill-conditioned) models of structural engineering practice. With this original approach, a new iterative solution strategy has been opened.

• Structural Engineering and Mechanics
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• 제88권5호
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• pp.439-449
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• 2023

Non-linear vibration characteristics of functionally graded CNT-reinforced composite (FG-CNTRC) cylindrical shell panel on elastic foundation have not been sufficiently examined. In this situation, this study aims at the profound numerical investigation of the non-linear vibration response of FG-CNTRC cylindrical panels on Winkler-Pasternak foundation by introducing an accurate and effective 2-D meshfree-based non-linear numerical method. The large-amplitude free vibration problem is formulated according to the first-order shear deformation theory (FSDT) with the von Karman non-linearity, and it is approximated by Laplace interpolation functions in 2-D natural element method (NEM) and a non-linear partial derivative operator H_NL. The complex and painstaking numerical derivation on the curved surface and the crucial shear locking are overcome by adopting the geometry transformation and the MITC3+ shell elements. The derived nonlinear modal equations are iteratively solved by introducing a three-step iterative solving technique which is combined with Lanczos transformation and Jacobi iteration. The developed non-linear numerical method is estimated through the benchmark test, and the effects of foundation stiffness, CNT volume fraction and functionally graded pattern, panel dimensions and boundary condition on the non-linear vibration of FG-CNTRC cylindrical panels on elastic foundation are parametrically investigated.

• 한국전자통신학회논문지
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• 제10권7호
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• pp.793-800
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• 2015

이동 로봇 Pan-Tilt 기구부에 장착된 스테레오 카메라의 Head-Eye 보정 및 Wheel 보정을 동시에 수행하는 방법을 제안한다. 카메라가 이동로봇의 고정형 기구부에 장착되어있는 경우를 고려한 기존의 방법들은 최근 일반적인 이러한 시스템에 적용될 수 없다. 이러한 문제점을 해결하기 위하여 본 논문에서는 기존 방법을 바탕으로 한 선형 반복적인 방법을 고안하였다. 이것은 동시보정을 통한 효율성뿐만 아니라 정확도 면에서도 만족할만한 결과를 얻었다. 그리고 비선형 최적화 기법을 통해 보다 높은 정확도의 보정을 구현했다.

• 조명전기설비학회논문지
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• 제17권5호
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• pp.88-93
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• 2003

본 논문에서는 반복법에 의한 쌍선형 시스템의 제어기 설계방법을 제안한다. 보조수열을 갖는 반복과정은 쌍선형 시스템으로부터 선형시변 시스템을 구성하는 과정에서 정의되고, 최적의 2차 가격함수를 갖는 쌍선형 시스템에서 궤환 제어기를 설계하기 위한 최적화 과정이 Riccati 접근법과 관련된 표현에 의해 주어진다. 제안된 방법에 의해서 개선된 성능과 우수한 수렴성이 성취됨을 시뮬레이션 결과에서 보인다.

• International Journal of Control, Automation, and Systems
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• 제6권2호
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• pp.269-277
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• 2008

This paper proposes a necessary and sufficient condition of convergence in the $L_2$-norm sense for a feedback-based iterative learning control (ILC) system including a multi-input multi-output (MIMO) linear time-invariant (LTI) plant. It is shown that the convergence conditions for a nominal plant and an uncertain plant are equal to the nominal performance condition and the robust performance condition in the feedback control theory, respectively. Moreover, no additional effort is required to design an iterative learning controller because the performance weighting matrix is used as an iterative learning controller. By proving that the least upper bound of the $L_2$-norm of the remaining tracking error is less than that of the initial tracking error, this paper shows that the iterative learning controller combined with the feedback controller is more effective to reduce the tracking error than only the feedback controller. The validity of the proposed method is verified through computer simulations.

• 호남수학학술지
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• 제32권3호
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• pp.399-412
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• 2010

In this paper, we consider a preconditioned accelerated overrelaxation (PAOR) method to solve systems of linear equations. We show the convergence of the PAOR method. We also give com-parison results when the coefficient matrix is an L- or H-matrix. Finally, we provide some numerical experiments to show efficiency of PAOR method.