• 한국지구물리탐사학회:학술대회논문집
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• 2006.06a
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• pp.131-135
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• 2006

A seismic waveform inversion for prestack seismic data based on the Gauss-Newton method is presented. The Gauss-Newton method for seismic waveform inversion was proposed in the 80s but has rarely been studied. Extensive computational and memory requirements have been principal difficulties. To overcome this, we used different sizes of grids in the inversion stage from those of grids in the wave propagation simulation, temporal windowing of the simulation and approximation of virtual sources for calculating partial derivatives, and implemented this algorithm on parallel supercomputers. We show that the Gauss-Newton method has high resolving power and convergence rate, and demonstrate potential applications to real seismic data.

• Journal for History of Mathematics
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• v.29 no.4
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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 Mathematical Society
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• v.53 no.6
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• pp.1371-1389
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• 2016

In this paper, we propose a new rank two quasi-Newton method based on adjoint Broyden updates for solving symmetric nonlinear equations, which can be seen as a class of adjoint BFGS method. The new rank two quasi-Newton update not only can guarantee that $B_{k+1}$ approximates Jacobian $F^{\prime}(x_{k+1})$ along direction $s_k$ exactly, but also shares some nice properties such as positive deniteness and least change property with BFGS method. Under suitable conditions, the proposed method converges globally and superlinearly. Some preliminary numerical results are reported to show that the proposed method is effective and competitive.

• Journal of Advanced Marine Engineering and Technology
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• v.24 no.1
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• pp.18-24
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• 2000

As ship's propulsion shafting system has been complicated, many linear methods that have been used until now are not sufficient enough to produce proper solutions and these solutions are ofter unreasonable. So we need to solve nonlinear systems, and many methods for solving nonlinear vibration system have been developed. In this study, the propulsion shafting system was modeled with Duffing's nonlinear vibration system and multi-degree-of-freedom, and analyzed by using Quasi-Newton method. And for the purpose of confirming the reliability of the calculating results for nonlinear forced torsional vibration of the propulsion shafting system, the nonlinear calculated results were compared with the linear calculated ones for ship's propulsion shafting system. In the result, for analysis of the forced torsional vibration of the propulsion systems with nonlinear elements, the modified Newton's method is confirmed reasonable.

• East Asian mathematical journal
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• v.24 no.2
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• pp.151-159
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• 2008

An error analysis introduced in [1], [2] is utilized in combination with nondiscrete mathematical induction to provide a finer than before [3]-[7], [11] semilocal convergence analysis for a certain class of modified Newton processes.

• International Journal of Reliability and Applications
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• v.4 no.1
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• pp.41-50
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• 2003

This paper represents the first comprehensive comparison of the Newton-Raphson's method and Simple Iterative Procedure (SIP) in the maximum likelihood estimation of the two-parameter Weibull distribution. Computer simulation is employed to compare these two methods for multiply censored, singly censored data (Type I or Type Ⅱ censoring) and complete data. Results indicate the Newton-Raphson's with the Menon's estimated value, as an initial point remains the effective iterative procedure for estimating the parameters.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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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.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.1394-1395
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• 2011

Now a days has problem of energy resource shortage and environmental pollution. We are looking up various solution plans regarding this problem. Solar power is one of the solution to solve the energy shortage problem. But solar power is affected by the weather. So variation weather we can use Maximum Power Point Tracing device for solar PV system. In this paper, New MPPT method is proposed to tracking MPP at low and high insolation by combining constant voltage method with Newton Method method.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.3
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• pp.294-299
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• 2005

This paper presents the separation performance of the linearly mixed image signals with additive noises by using an independent component analyses(ICAs) of the fixed-point(FP) algorithm based on Newton and secant method, respectively. The Newton's FP-ICA uses the slope of objective function, and the secant's FP-ICA also uses the tangent line of objective function. The 2 kinds of ICA have been applied to the 2 dimensional 2-image with $512\times512$ pixels. Then Gaussian noise and Laplacian noise are added to the mixed images, respectively. The experimental results show that the Newton's FP-ICA has better the separation speed than secant FP-ICA and the secant's FP-ICA has also the better separation rate than Newton's FP-ICA. Especially, the Newton and secant method gives relatively larger improvement degree in separation speed and rate as the noise increases.