• 한국전자파학회논문지
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• 제28권11호
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• pp.880-885
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• 2017

기존에 제안된 AD-MUSIC 알고리즘을 이용하여 2차원 탐색 없이 1차원 탐색을 반복함으로써 DOD/DOA 추정이 가능하다. 본 논문에서는 계산량을 더욱 감소하기 위해 1차원 탐색에 Newton 기반 기법을 적용한다. 본 논문은 바이스태틱 MIMO 레이다 시스템의 수신신호 모델링과 AD-MUSIC의 유도과정을 보이고, 뉴턴 반복 기법을 AD-MUSIC에 적용한다. 추정 시, 기존의 AD-MUSIC 알고리즘의 성능과 계산량이 탐색 간격에 영향을 받는 것에 반해, AD-MUSIC의 성능과 뉴턴기법을 적용하는 본 논문의 방법인 경우, 탐색 간격에 관계없이 우수한 성능을 보이고, 계산량 또한 감소하는 효과를 보인다는 것을 시뮬레이션을 통해 보인다.

• 한국전산구조공학회논문집
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• 제18권4호통권70호
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• pp.385-393
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• 2005

본 논문에서는 기하학적으로 비선형인 유연한 Timoshenko 보의 대변위 운동방정식에 유한요소를 사용하여 정식화하였다. 비선형 구속방정식은 라그랑지 상수를 이용하여 운동방정식에 통합되었다. 정식화하는 과정과 수치해석에서 선형과 비선형 영향을 파악하였고, 코리올리스(Coriolis)힘과 회전자(Gyroscopic)힘의 효과는 관성력과 감쇠력과는 달리 일반적인 외력으로 간주하여 해석할 수 있었다. Newmark의 시간적분과 Newton-Raphson 반복법을 사용한 수치예제를 통해 정식화의 효용성을 보여주었다.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.393-406
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• 1999

Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods. The first uses conditions on the first Frechet-derivative whereas the second theorem employs hypotheses on the second. Radius of con-vergence as well as rate of convergence results are derived. Results involving superlinear convergence and known to be true for inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivation our radius of convergence results are derived. Results involving superlinear convergence and known to be true or inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivative our radius of conver-gence is larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also pro-vided to show that our radius of convergence is larger then the one in [10].

• 한국수학사학회지
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• 제29권4호
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• pp.243-254
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• 2016

This research identifies the elements of the methodologies of Newton's discovery of his dynamics. These methodologies involve the transformation of preceding theoretical concepts and the discovery of common cause. This essay consists of two parts within historical case studies of Newton's works. The elements of the method of discovery consists of the transformation of preceding concepts and the identification of common cause in the formation of the research program's hard cores and protective belts. Newton transformed their predecessors' concepts to find out appropriate common causes in his dynamical theory. The transformed theoretical concepts are synthesized to be constructed as the elements of common cause which provide the foundations of Newtonian research programs.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.101-115
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• 2001

Recent theoretical analysis of numerical methods for solving nonlinear systems of equations is represented by alpha theory of Newton method developed Smale et al. The theory was extended to Secant method by providing convergence conditions by Yakoubsohn which the Secant method is treated as an operator defined for analytical functions. We use Secant methods as an iterative scheme with approximations, which results in new convergence conditions. We compare the two conditions and show that the new conditions represent the features of Secant method in a more precise way.

• 한국자동차공학회논문집
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• 제9권1호
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• pp.156-162
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• 2001

An effective and practical method is presented for solving the forward kinematics of a 6-DOF Stewart Platform, using neural network algorithm together with Newton-Raphson method. An approximated solution is obtained from trained neural network, then it is used as an initial estimate for Newton-Raphson method. A series of accurate solutions are calculated with reasonable speed for the entire workspace of the platform. The solution procedure can be used for driving a real-time simulation platform.

• 제어로봇시스템학회논문지
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• 제13권7호
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• pp.683-687
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• 2007

In last decades, several linearization methods for the AOA measurements have been proposed, for example, Gauss-Newton method and Closed-Form solution. Gauss-Newton method can achieve high accuracy, but the convergence of the iterative process is not always ensured if the initial guess is not accurate enough. Closed-Form solution provides a non-iterative solution and it is less computational. It does not suffer from convergence problem, but estimation error is somewhat larger. This paper proposes a Self-Tuning Weighted Least Square AOA algorithm that is a modified version of the conventional Closed-Form solution. In order to estimate the error covariance matrix as a weight, a two-step estimation technique is used. Simulation results show that the proposed method has smaller positioning error compared to the existing methods.

• 충청수학회지
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• 제22권2호
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• pp.217-227
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• 2009

Assuming that a given nonlinear function f : $\mathbf{R}{\rightarrow}\mathbf{R}$ has a zero $\alpha$with integer multiplicity $m{\geq}1$ and is sufficiently smooth in a small neighborhood of $\alpha$, we define extended leap-frogging Newton's method. We investigate the order of convergence and the asymptotic error constant of the proposed method as a function of multiplicity m. Numerical experiments for various test functions show a satisfactory agreement with the theory presented in this paper and are throughly verified via Mathematica programming with its high-precision computability.

• 대한수학회지
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• 제50권4호
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• pp.755-770
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• 2013

One of the interesting nonlinear matrix equations is the quadratic matrix equation defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix, and A, B and C are $n{\times}n$ given matrices with real elements. Another one is the matrix polynomial $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m=0,\;X,\;A_i{\in}\mathbb{R}^{n{\times}n}$$. Newton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P(X). The method does not depend on the singularity of the Fr$\acute{e}$chet derivative. Finally, we give some numerical examples.

• 한국철도학회논문집
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• 제12권2호
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• pp.236-242
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• 2009

본 연구에서는 철도차량의 차륜과 레일에 대해 플랜지 접촉을 포함하여 모든 위치예서 차륜-레일간 접촉 위치를 수치 해석적으로 구하는 방범을 제안한다. 이를 위해 차륜과 레일의 형상은 매개변수로 표현되는 3차원 곡면함수로 나타내었다. 기구학적 구속조건식을 Newton-Rhapson 방법을 이용하여 구하는 것과 차륜과 레일간 최소거리가 0이 된다는 최적화 방법을 동시에 이용하여 정확하고 효율적으로 계산하는 새로운 방법을 제안하였다.