• Proceedings of the KIEE Conference
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• 1992.07a
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• pp.205-210
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• 1992

The power flow calculations are the most important and powerful tools in the various studies of power system engineering. Newton-Raphson method, among the various power flow calculation techniques, is normally used due to its rapidness of numerical convergency. In the conventional Newton-Raphson method, however, there are some unrealistic assumptions, in which all the system power losses are considered to be supplied by the slack bus generator. Introducing the system power loss formula and augmenting the conventional Newton-Raphson power flow method, we can relieve the unrealistic assumption and improve the performance of power flow calculation. In this study, A new approach for handling the losses and augmenting the conventional power flow problem is proposed. The proposed method estimates the increamental changes of active power on each generation bus with respect to the change of total system power losses and the estimated value are used to update the slack bus power. If some studies for more theoritical investigations and verifications are followed, the proposed approach will show some improvement of the conventional method and give lots of contribution to increase the performance of power flow techniques in power systems engineering.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.4
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• pp.223-231
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• 2013

This paper presents a time-domain Gauss-Newton full-waveform inversion method for the material profile reconstruction in heterogeneous semi-infinite solid media. To implement the inverse problem in a finite computational domain, perfectly-matchedlayers( PMLs) are introduced as wave-absorbing boundaries within which the domain's wave velocity profile is to be reconstructed. The inverse problem is formulated in a partial-differential-equations(PDE)-constrained optimization framework, where a least-squares misfit between measured and calculated surface responses is minimized under the constraint of PML-endowed wave equations. A Gauss-Newton-Krylov optimization algorithm is utilized to iteratively update the unknown wave velocity profile with the aid of a specialized regularization scheme. Through a series of one-dimensional examples, the solution of the Gauss-Newton inversion was close enough to the target profile, and showed superior convergence behavior with reduced wall-clock time of implementation compared to a conventional inversion using Fletcher-Reeves optimization algorithm.

• Proceedings of the Korea Institute of Applied Superconductivity and Cryogenics Conference
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• 2002.02a
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• pp.330-333
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• 2002

This study is concerned with the optimal design of DC reactor type high-Tc superconducting fault current limiter(SFCL) by Newton method. What should be first thought over in developing SFCL is the condition in which the cost function is minimized under given constraints. So, this condition is supposed to be the values corresponding to the variables the cost function counts on. In this paper, we got the result for the SFCL available at the level of 6.6kV-200A by means of simulation.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.117-123
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• 2012

We provide a convergence analysis of Newton's method for set valued maps under center H$\ddot{o}$lder continuity conditions on the Fr$\acute{e}$chet derivative of the operator involved. This approach extends the applicability of earlier works [4,5,7].

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.13-18
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• 2009

A semilocal convergence analysis is provided for Newton's method in a Banach space. The inverses of the operators involved are only locally $H{\ddot{o}}lderian$. We make use of a point-based approximation and center-$H{\ddot{o}}lderian$ hypotheses for the inverses of the operators involved. Such an approach can be used to approximate solutions of equations involving nonsmooth operators.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.483-492
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• 2008

The k-fold pseudo-Newton's method is proposed and its convergence behavior is investigated near a simple zero. The order of convergence is proven to be at least k + 2. The asymptotic error constant is explicitly given in terms of k and the corresponding simple zero. High-precison numerical results are successfully implemented via Mathematica and illustrated for various examples.

• East Asian mathematical journal
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• v.24 no.3
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• pp.295-304
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• 2008

We approximate a locally unique solution of a nonlinear operator equation containing a non-differentiable operator in a Banach space setting using Newton's method. Sufficient conditions for the semilocal convergence of Newton's method in this case have been given by several authors using mainly increasing sequences [1]-[6]. Here, we use center as well as Lipschitz conditions and decreasing majorizing sequences to obtain new sufficient convergence conditions weaker than before in many interesting cases. Numerical examples where our results apply to solve equations but earlier ones cannot [2], [5], [6] are also provided in this study.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.307-319
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• 2010

We provide a new semilocal convergence analysis of the Gauss-Newton method (GNM) for solving nonlinear equation in the Euclidean space. Using our new idea of recurrent functions, and a combination of center-Lipschitz, Lipschitz conditions, we provide under the same or weaker hypotheses than before [7]-[13], a tighter convergence analysis. The results can be extented in case outer or generalized inverses are used. Numerical examples are also provided to show that our results apply, where others fail [7]-[13].

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.111-120
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• 2008

A semi local convergence analysis is provided for Newton's method in a Banach space setting. The operators involved are only locally Holderian. We make use of a point-based approximation and center-Holderian hypotheses. This approach can be used to approximate solutions of equations involving nonsmooth operators.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.211-225
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• 2014

A new class of smoothing functions is introduced in this paper, which includes some important smoothing complementarity functions as its special cases. Based on this new smoothing function, we proposed a smoothing Newton method. Our algorithm needs only to solve one linear system of equations. Without requiring the nonemptyness and boundedness of the solution set, the proposed algorithm is proved to be globally convergent. Numerical results indicate that the smoothing Newton method based on the new proposed class of smoothing functions with ${\theta}{\in}(0,1)$ seems to have better numerical performance than those based on some other important smoothing functions, which also demonstrate that our algorithm is promising.