• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.345-360
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• 2001

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 mth(m≥2 an integer). Radius of convergence 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 mth Frechet-derivative our radius of convergence can sometimes be larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also provided to show that our radius of convergence is larger than the one in [10].

• Economic and Environmental Geology
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• v.22 no.3
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• pp.267-276
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• 1989

This paper presents results of interpretaton of gravity data by iterative nonlinear inversion methods. The gravity data are obtained by a theoretical formula for two-dimensional 2-layer structure. Depths to the basement of the structure are determined from the gravity data by four interative inversion methods. The four inversion methods used here are the Gradient, Gauss-Newton, Newton-Raphson, and Full Newton methods. Inversions are performed by using different initial guesses of depth for the over-determined, even-determined, and under-determined cases. This study shows that the depth can be determined well by all of the methods and most efficiently by the Newton-Raphson method.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.6
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• pp.34-44
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• 1994

In this paper, an iterative inversion method in angular spectral domain is presented for microwave imaging of a perfectly conducting cylinder. Angular spectra are calculated from measured far-field scattered fields. And then both the propagating modes and the evanescent modes are defined. The center and initial shape of an unknown conductor may be obtained by the characteristics of angular spectra and the total scattering cross section (TSCS). Finally, the orignal shape is reconstructed by the modified Newton algorithm. By using well estimated initial shape the local minima can be avoided, which might appear when the nonlinear equation is solved with Newton algorithm. It is shown to be robust to noise in scattered fields via numerical examples by keeping only the propagating modes and filtering out the evanescent modes.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.12A
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• pp.1978-1982
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• 2001

In a Multi-carrier modulation system, CP (Cyclic prefix) is inserted in the transmit tame in order to eliminate the ISI (Intersymbol Interference) and ICI (Interchannel Interference) caused by delay spread of a received signal, which in rum degrades the throughput of the system. TEQ (Time-domain equalizer) improves the system throughput by shortening the CIR (Channel Impulse Response) time and maintaining the CP length to the minimum regardless of the channel condition. In this paper, a new MMSE (Minimum Mean Square Error) TEQ algorithm is proposed and its performance is analyzed in order to speed up computing the optimum tap coefficients of the equalizer by employing Newton method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.4
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• pp.675-691
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• 2002

The focus of this work is on the development of large-scale numerical optimization methods for optimal control of steady incompressible Navier-Stokes flows. The control is affected by the suction or injection of fluid on portions of the boundary, and the objective function of fluid on portions of the boundary, and the objective function represents the rate at which energy is dissipated in the fluid. We develop reduced Hessian sequential quadratic programming. Both quasi-Newton and Newton variants are developed and compared to the approach of eliminating the flow equations and variables, which is effectively the generalized reduced gradient method. Optimal control problems we solved for two-dimensional flow around a cylinder. The examples demonstrate at least an order-of-magnitude reduction in time taken, allowing the optimal solution of flow control problems in as little as half an hour on a desktop workstation.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.395-411
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• 2012

Several methods with order higher than that of Newton methods which are of order 2 have been reported in literature for solving nonlinear equations. The focus of most of these methods was to economize on/minimize the number of function evaluations per iterations. We have demonstrated here that there are several computational pit-falls, such as the violation of fixed-point theorem, that one could encounter while using these methods. Further it was also shown that the overall computational complexity could be more in these high-order methods than that in the second-order Newton method.

• East Asian mathematical journal
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• v.27 no.3
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• pp.319-337
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• 2011

We approximate a locally unique solution of a nonlinear equation in a Banach space setting using an inexact two-step Newton-type method. It turn out that under our new idea of recurrent functions, our semilocal analysis provides tighter error bounds than before, and in many interesting cases, weaker sufficient convergence conditions. Applications including the solution of nonlinear Chandrasekhar-type integral equations appearing in radiative transfer and two point boundary value problems are also provided in this study.

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.1680-1681
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• 2007

This paper deals with RLS algorithm using Newton-Raphson method based adaptive forgetting factor for a passive telemetry RF sensor system in order to estimate the time variant parameter to be included in RF sensor model.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.1-27
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• 2010

Wu and Zhao [17] provided a semilocal convergence analysis for a Newton-type method on a Banach space setting following the ideas of Frontini and Sormani [9]-[11]. In this study first: we point out inconsistencies between the hypotheses of Theorem 1 and the two examples given in [17], and then, we provide the proof in affine invariant form for this result. Then, we also establish new convergence results with the following advantages over the ones in [17]: weaker hypotheses, and finer error estimates on the distances involved. A numerical example is also provided to show that our results apply in cases other fail [17].

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.279-282
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• 2007

Using the center instead of the Lipschitz condition we show how to provide weaker sufficient convergence conditions of the modified Newton Kantorovich method for the solution of nonlinear singular integral equations with Curleman shift (NLSIES). Finer error bounds on the distances involved and a more precise information on the location of the solution are also obtained and under the same computational cost than in [1].