• 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 for History of Mathematics
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• v.30 no.3
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• pp.185-199
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• 2017

In tropical geometry, the sum of two numbers is defined as the minimum, and the multiplication as the sum. As a way to build tropical plane curves, we could use Newton polygons or amoebas. We study one method to convert the representation of an algebraic variety from an image of a rational map to the zero set of some multivariate polynomials. Mikhalkin proved that complex curves can be replaced by tropical curves, and induced a combination formula which counts the number of tropical curves in complex projective plane. In this paper, we present close examinations of this particular combination formula.

• East Asian mathematical journal
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• v.29 no.5
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• pp.511-519
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• 2013

There are various methods for evaluating a matrix square root, which is a solvent of the quadratic matrix equation $X^2-A=0$. We consider new iterative methods for solving matrix square roots of M-matrices. Particulary we show that the relaxed binomial iteration is more efficient than Newton-Schulz iteration in some cases. And we construct a formula to find relaxation coefficients through statistical experiments.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.103-112
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• 2005

Using the Newton's identities, we give the inductive formula for the generator polynomials of the $p$-adic quadratic residue codes.

• 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 Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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• pp.71-79
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• 1999

We consider multi-step quasi-Newton methods for unconstrained optimization. These methods were introduced by Ford and Moghrabi [1, 2], who showed how interpolating curves could be used to derive a generalization of the Secant Equation (the relation normally employed in the construction of quasi-Newton methods). One of the most successful of these multi-step methods makes use of the current approximation to the Hessian to determine the parameterization of the interpolating curve in the variable-space and, hence, the generalized updating formula. In this paper, we investigate new parameterization techniques to the approximate Hessian, in an attempt to determine a better Hessian approximation at each iteration and, thus, improve the numerical performance of such algorithms.

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.61-76
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• 1995

Much research has been done to estimate the magnitudes of the changes of the roots from the perturbed polynomials. For more information and references on such work, see [2, 4, 5, 10, 17].

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.423-430
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• 2002

The object of this Paper is to Present a q-analogue of the Newton's forward-difference interpolation formula. We relate the q-beta function and the q-gamma function by the q-difference operators.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.135-145
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• 1995

A new algorithm was given to successively fit the multiexponential function/nonlinear function to data by a weighted least squares method, using Gauss-Newton, Marquardt, gradient and DUD methods for convergence. This study also considers the problem of linear-nonlimear weighted least squares estimation which is based upon the usual Taylor's formula process.

• Journal of the Korean Data and Information Science Society
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• v.16 no.1
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• pp.127-136
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• 2005

We will derive some results on the perturbation of roots using Newton's interpolation formula. And we also compare our results with those obtained by Ostrowski by giving some numerical experiments with Wilkinson's polynomials.