• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.6
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• pp.751-759
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• 2007

We have developed several methods for the optimization problem having large-scale and highly nonlinear system. First, step by step method in optimization process was employed to improve the convergence. In addition, techniques of furnishing good initial guesses for analysis using sensitivity information acquired from optimization iteration, and of manipulating analysis/optimization convergency criterion motivated from simultaneous technique were used. We applied them to flow control problem and verified their efficiency and robustness. However, they are based on quasi-Newton method that approximate the Hessian matrix using exact first derivatives. However solution of the Navier-Stokes equations are very cost, so we want to improve the efficiency of the optimization algorithm as much as possible. Thus we develop a true Newton method that uses exact Hessian matrix. And we apply that to the three-dimensional problem of flow around a sphere. This problem is certainly intractable with existing methods for optimal flow control. However, we can attack such problems with the methods that we developed previously and true Newton method.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.393-406
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• 1999

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 second. Radius of con-vergence 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 second Frechet-derivation our radius of convergence results are derived. Results involving superlinear convergence and known to be true or inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivative our radius of conver-gence is larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also pro-vided to show that our radius of convergence is larger then the one in [10].

• Korean Journal of Computational Design and Engineering
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• v.3 no.3
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• pp.183-191
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• 1998

There are many available algorithms based on the different approaches to solve the intersection problems between two curves. Among them, the implicitization method is frequently used since it computes precise solutions fast and is robust in lower degrees. However, once the degrees of curves to be intersected are higher than cubics, its computation time increases rapidly and the numerical stability gets worse. From this observation, it is natural to transform the original problem into a set of easier ones. Therefore, curves are subdivided appropriately depending on their geometric behavior and approximated by a set of rational quadratic Bezier cures. Then, the implicitization method is applied to compute the intersections between approximated ones. Since the solutions of the implicitization method are intersections between approximated curves, a numerical process such as Newton-Raphson iteration should be employed to find true intersection points. As the seeds of numerical process are close to a true solution through the mix-and-match process, the experimental results illustrates that the proposed algorithm is superior to other algorithms.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.139-159
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• 2000

In this manuscript we study perturbed Newton-like methods for the solution of nonlinear operator equations in a Banach space and their discretized versions in connection with the mesh independence principle. This principle asserts that the behavior of the discretized process is asymptotically the same as that for the original iteration and consequently, the number of steps required by the two processes to converge to within a given tolerance is essentially the same. So far this result has been proved by others using Newton's method for certain classes of boundary value problems and even more generally by considering a Lipschitz uniform discretization. In some of our earlierpapers we extend these results to include Newton-like methods under more general conditions. However, all previous results assume that the iterates can be computed exactly. This is mot true in general. That in why we use perturbed Newton-like methods and even more general conditions. Our results, on the one hand, extend, and on the other hand, make more practical and applicable all previous results.

• Journal of the Korean Society for Railway
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• v.12 no.2
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• pp.236-242
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• 2009

This paper presents a numerical analysis method to determine flange contact at variable wheel positions. The shapes of the wheel and rail surface functions with surface parameters. The Newton-Rhapson method for wheel-rail contact can provide fast solutions, but may not yield true values at optimization process with the condition that minimum distance is zero can time-consuming. A compound method, combining the Newton-Rhapson methods the optimization process method is proposed to provide exact solutions efficiently.

• 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].

• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.429-440
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• 2006

In statistical computing, it is often for researchers to need the distribution of a weighted sum of noncentral chi-square variables. In this case, it is very limited to know its exact distribution. There are many works to contribute to this topic, e.g. Imhof (1961) and Solomon-Stephens (1977). Imhof's method gives good approximation to the true distribution, but it is not easy to apply even though we consider the development of computer technology Solomon-Stephens's three moment chi-square approximation is relatively easy and accurate to apply. However, they skipped many details, and their simulation is limited to a weighed sum of central chi-square random variables. This paper gives details on Solomon-Stephens's method. We also extend their simulation to the weighted sum of non-central chi-square distribution. We evaluated approximated powers for homogeneous test and compared them with the true powers. Solomon-Stephens's method shows very good approximation for the case.

• Geophysics and Geophysical Exploration
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• v.6 no.2
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• pp.95-100
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• 2003

In this study, we developed reflection tomography inversion algorithm using Straight Ray Technique (SRT) which can calculate travel time easily and fast for complex geological structure. The inversion process begins by setting the initial velocity model as a constant velocity model that hat only impedance boundaries. The inversion process searches a layer-interface structure model that is able to explain the given data satisfactorily by inverting to minimize data misfit. For getting optimal solution, we used Gauss-Newton method that needed constructing the approximate Hessian matrix. We also applied the Marquart-Levenberg regularization method to this inversion process to prevent solution diverging. The ability of the method to resolve typical target structures was tested in a synthetic salt dome inversion. Using the inverted velocity model, we obtained the migration image close to that of the true velocity model.

• Computational Structural Engineering
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• v.9 no.2
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• pp.121-131
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• 1996

This work proposes an optimality criteria applicable to the optimum design of plane frames subject to multiple behavioral constraints on member stresses and lateral displacements of nodes and also to side constraints on design variables. The method makes use of a first order approximation for both deflection and stress constraints instead of the zero order approximation based on the concept of FSD (fully stressed design). A redesign algorithm is derived from a mathematically rigorous method which uses the Newton-Raphson method to solve the system of nonlinear constraint equations and reduces the design space whenever minimum size restrictions become active. When applied to worked examples it proved more accurate and efficient, and it is often found that optimum designs are not fully stressed designs. This fact suggests that this rigorous method is worth what it claims for complicated computing and thus had better replace the crude stress ratio algorithm adopted by the majority of optimality criteria approaches. This is particularly true as long as we enjoy ever-increasing computing power at negligible costs.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.329-336
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• 2007

For scaling of the gradient of misfit function, we develop a new pseudo-Hessian matrix constructed by combining amplitude field and pseudo-Hessian matrix. Since pseudo- Hessian matrix neglects the calculation of the zero-lag auto-correlation of impulse responses in the approximate Hessian matrix, the pseudo-Hessian matrix has a limitation to scale the gradient of misfit function compared to the approximate Hessian matrix. To validate the new pseudo- Hessian matrix, we perform frequency-domain elastic full waveform inversion using this Hessian matrix. By synthetic experiments, we show that the new pseudo-Hessian matrix can give better convergence to the true model than the old one does. Furthermore, since the amplitude fields are intrinsically obtained in forward modeling procedure, we do not have to pay any extra cost to compute the new pseudo-Hessian. We think that the new pseudo-Hessian matrix can be used as an alternative of the approximate Hessian matrix of the Gauss-Newton method.