• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2003년도 춘계학술대회 논문집
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• pp.1545-1548
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• 2003

In rigid-plastic finite element method, there is a heavy computation time and convergence problem. In this study. static-explicit rigid-plastic finite element method will be introduced. This method is the way that restrict the convergence interval. In result, convergence problem and computation time due to large non-linearity in the existing numerical analysis method were no longer a critical problem. Also, we investigated the effect of punch stroke and the strain increment this method. It is expected that various results from the numerical analysis will give very useful information for the design of tools in sheet metal forming process.

• 대한수학회지
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• 제51권1호
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• pp.137-162
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• 2014

In this work we study the local and semilocal convergence of the relaxed Newton's method, that is Newton's method with a relaxation parameter 0 < ${\lambda}$ < 2. We give a Kantorovich-like theorem that can be applied for operators defined between two Banach spaces. In fact, we obtain the recurrent sequence that majorizes the one given by the method and we characterize its convergence by a result that involves the relaxation parameter ${\lambda}$. We use a new technique that allows us on the one hand to generalize and on the other hand to extend the applicability of the result given initially by Kantorovich for ${\lambda}=1$.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.239-254
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• 2006

An efficient descent method for unconstrained optimization problems is line search method in which the step size is required to choose at each iteration after a descent direction is determined. There are many ways to choose the step sizes, such as the exact line search, Armijo line search, Goldstein line search, and Wolfe line search, etc. In this paper we propose a new inexact line search for a general descent method and establish some global convergence properties. This new line search has many advantages comparing with other similar inexact line searches. Moreover, we analyze the global convergence and local convergence rate of some special descent methods with the new line search. Preliminary numerical results show that the new line search is available and efficient in practical computation.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.763-771
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• 2009

T.H. Kim, H.K. Xu, [Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal.(2007),doi:l0.l016/j.na.2007.02.029.] proved the strong convergence for asymptotically strict pseudo-contractions by the classical CQ iterative method. In this paper, we apply the monotone CQ iterative method to modify the classical CQ iterative method of T.H. Kim, H.K. Xu, and to obtain the strong convergence theorems for asymptotically strict pseudo-contractions. In the proved process of this paper, Cauchy sequences method is used, so we complete the proof without using the demi-closedness principle, Opial's condition or others about weak topological technologies. In addition, we use a ingenious technology to avoid defining that F(T) is bounded. On the other hand, we relax the restriction on the control sequence of iterative scheme.

• 대한수학회논문집
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• 제37권4호
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• pp.1009-1023
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• 2022

The main objective of this work is to investigate the study of the local and semi-local convergence of the contraharmonic-mean Newton's method (CHMN) for solving nonlinear equations in a Banach space. We have performed the semi-local convergence analysis by using generalized conditions. We examine the theoretical results by comparing the CHN method with the Newton's method and other third order methods by Weerakoon et al. using some test functions. The theoretical and numerical results are also supported by the basins of attraction for a selected test function.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.507-516
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• 1998

In this study we are concerned with the problem of ap-proximating a locally unique solution of an equation on a Banach space. A semilocal convergence theorem is given for the Super-Halley method in Banach spaces. Earlier results have shown that the order of convergence is four for a certain class of operators [4] [5] [8] These results were not given in affine invariant form and made use of a real quadratic majorizing polynomial. Here we provide our re-sults in affine invariant form showing that the order of convergence is at least four. In cases that it is exactly four the rate of convergence is improved. We achieve these results by using a cubic majorizing polynomial. Some numerical examples are given to show that our error bounds are better than earlier ones.

• 대한수학회보
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• 제56권3호
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• pp.621-629
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• 2019

In this paper, we present a local convergence analysis of a three point method with convergence order $1.839{\ldots}$ for approximating a locally unique solution of a nonlinear operator equation in setting of Banach spaces. Using weaker hypotheses than in earlier studies, we obtain: larger radius of convergence and more precise error estimates on the distances involved. Finally, numerical examples are used to show the advantages of the main results over earlier results.

• 정보처리학회논문지A
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• 제11A권2호
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• pp.203-206
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• 2004

저자는 등각사상을 구하기 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 수렵하지 않는 불안정현상의 원인을 분석하여 저주파필터를 적용한 새로운 반복법을 제안하였다. 원래의 Wegmann 반복법으로는 발산하는 모튼 문제에 있어서 새로 제안한 방법에 의해서 수렴하는 수치실험 결과를 얻었는데 본 논문에서는 저주파필터를 적용한 Wegmann해법에 의해 실험적으로 수렴한 결과를 Fourier 분석기법에 의해 이론적으로 증명한다.

• Journal of applied mathematics & informatics
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• 제34권1_2호
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• pp.157-165
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• 2016

In this paper, we develop a new hybridization conjugate gradient method for solving the unconstrained optimization problem. Under mild assumptions, we get the sufficient descent property of the given method. The global convergence of the given method is also presented under the Wolfe-type line search and the general Wolfe line search. The numerical results show that the method is also efficient.

• 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.