• East Asian mathematical journal
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• 제25권2호
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• pp.153-157
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• 2009

Motivated by optimization considerations we revisit the work by Dontchev in [7] involving the convergence of Newton's method to a solution of a generalized equation in a Banach space setting. Using the same hypotheses and under the same computational cost we provide a finer convergence analysis for Newton's method by using more precise estimates.

• East Asian mathematical journal
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• 제26권3호
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• pp.365-370
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• 2010

A local convergence result is provided for the continuous analog of Newton's method in a Banach space setting. The radius of convergence is larger, the error bounds tighter, and under the same or weaker hypotheses than before [12].

• East Asian mathematical journal
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• 제24권2호
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• pp.161-168
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• 2008

We revisit the study of finding solutions of equations containing a differentiable and a continuous term on a Banach space setting [1]-[5], [9]-[11]. Using more precise majorizing sequences than before [9]-[11], we provide a semilocal convergence analysis for the generalized Newton's method as well the generalized modified Newton's method. It turns out that under the same or even weaker hypotheses: finer error estimates on the distances involved, and an at least as precise information on the location of the solution can be obtained. The above benefits are obtained under the same computational cost.

• 대한수학회지
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• 제51권2호
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• pp.251-266
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• 2014

In this paper, we use Newton's method to approximate a locally unique solution of an equation in Banach spaces and introduce recurrent functions to provide a weaker semilocal convergence analysis for Newton's method than before [1]-[13], in some interesting cases, provided that the Fr$\acute{e}$chet-derivative of the operator involved is p-H$\ddot{o}$lder continuous (p${\in}$(0, 1]). Numerical examples involving two boundary value problems are also provided.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1997년도 하계학술대회 논문집 D
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• pp.1094-1096
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• 1997

이제까지 전력계통의 상태를 알기 위한 조류계산은 전력방정식에 대한 직접적인 풀이로써 이루어졌다. 그런데 만일 자코비안 행열이 singular나 유사 singular가 된다면 그 전력 방정식의 해를 구할 수가 없게 된다. singular나 유사 singular가 되는 자코비안 행열을 가지는 전력방정식을 풀기 위하여 보조 방정식을 추가하여 미분불능인 점을 미분가능으로 변환하는 continuous method가 있다. 그런데 continuous method에서 보조 방정식은 원함수의 성질에 따라 달라지므로 어떤 일반적인 형태를 가지지 않는다. 따라서 본 논문에서는 전력방정식을 제약조건으로 가지고 부하 모선의 전력이 수용가의 요구량과 거의 일치되도록 하는 것을 목적 함수로 하는 최적화 문제로 조류계산을 변환하여 풀이하였다. 이러한 최적화 기법을 이용함으로써 continuous method에서 보조방정식이 원함수에 따라 계속적으로 변하는 문제를 개선하였다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.60.4-60
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• 2001

Electrical impedance tomograpy (EIT) determines the resistivity distribution inside an inhomogeneous target by means of voltage and current measurements conducted at the target boundary. In this paper, a genetic algorithm (GA) approach is proposed for the solution of the EIT image reconstruction. Results of numerical experiments of EIT solved by the GA approach are presented and compared to that obtained by the modified Newton-Raphson method. The GA approach is relatively expensive in terms of computing time and resources, and at present this limits the applicability of GA to the field of static imaging. However, the continuous and rapid growth of computing resources makes the development of real-time dynamic imaging applications based on GA´s conceivable in the near future.