• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.747-760
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• 2014

In this paper a higher order iterative algorithm is developed for an unconstrained multivariate optimization problem. Taylor expansion of matrix valued function is used to prove the cubic order convergence of the proposed algorithm. The methodology is supported with numerical and graphical illustration.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1195-1209
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• 2009

In this paper, we point out some errors in a recent paper by Cordero and Torregrosa [7]. We prove the convergence of the variants of Newton's method for solving the system of nonlinear equations using two different approaches. Several examples are given, which illustrate the cubic convergence of these methods and verify the theoretical results.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.133-139
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• 2006

By combining the classical Newton's method with the pseudo-secant method, pseudo-secant-Newton's method is constructed and its order and rate of convergence are investigated. Given a function $f:\mathbb{R}{\rightarrow}\mathbb{R}$ that has a simple real zero ${\alpha}$ and is sufficiently smooth in a small neighborhood of ${\alpha}$, the convergence behavior is analyzed near ${\alpha}$ for pseudo-secant-Newton's method. The order of convergence is shown to be cubic and the rate of convergence is proven to be $\(\frac{f^{{\prime}{\prime}}(\alpha)}{2f^{\prime}(\alpha)}\)^2$. Numerical experiments show the validity of the theory presented here and are confirmed via high-precision programming in Mathematica.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.507-516
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• 1998

In this study we are concerned with the problem of ap-proximating a locally unique solution of an equation on a Banach space. A semilocal convergence theorem is given for the Super-Halley method in Banach spaces. Earlier results have shown that the order of convergence is four for a certain class of operators [4] [5] [8] These results were not given in affine invariant form and made use of a real quadratic majorizing polynomial. Here we provide our re-sults in affine invariant form showing that the order of convergence is at least four. In cases that it is exactly four the rate of convergence is improved. We achieve these results by using a cubic majorizing polynomial. Some numerical examples are given to show that our error bounds are better than earlier ones.

• Journal of Digital Convergence
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• v.12 no.12
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• pp.553-560
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• 2014

In this paper, we propose a method to convert 2D image to 3D anaglyph using quadratic & cubic B$\acute{e}$zier Curves in HTML5. In order to convert 2D image to 3D anaglyph image, we filter the original image to extract the RGB color values and create two images for the left and right eyes. Users are to set up the depth values of the image through the control point using the quadratic and cubic B$\acute{e}$zier curves. We have processed the depth values of 2D image based on this control point to create the 3D image conversion reflecting the value of the control point which the users select. All of this work has been designed and implemented in Web environment in HTML5. So we have made it for anyone who wants to create their 3D images and it is very easy and convenient to use.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1901-1906
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• 1995

The frequency response functions of systems incorporating a non-linear cubic stiffness subject to sinusoidal excitation are derived using the Volterra series and the convergence characteristics investigated. It is shown that the series representation of the frequency response functions converges only when the sinewave input amplitude is within a certain range. Within the range of convergence the frequency response function based on the Volterra series approaches the analytical one as more higher order frequency response function terms are included. Proposed is a criterion for the studies systems to predict approximately the range of sinewave input amplitude for which the series representation of the frequency response functions converges.

• Journal of Korea Multimedia Society
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• v.22 no.9
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• pp.1029-1035
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• 2019

In this paper, a tentative Kth order Goldschmidt floating point number Nth root algorithm for K order convergence rate in one iteration is proposed by applying Taylor series to the Goldschmidt square root algorithm. Using the proposed algorithm, Nth root and Nth inverse root can be computed from iterative multiplications without division. It also predicts the error of the algorithm iteration. It iterates until the predicted error becomes smaller than the specified value. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a floating point number Nth root unit.

• Journal of Digital Convergence
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• v.13 no.9
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• pp.209-218
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• 2015

Computer simulation plays an important role for a theoretical foundation in convergence technology and the interpolation is to know the unknown values from known values on grid points. Therefore it is an important problem to select an interpolation method for digital simulation. The aim of this paper is to compare analysis of interpolation methods for digital simulation. we test six different interpolation methods namely: Quartic-Lagrangian, Cubic Spline, Fourier, Hermit, PWENO and SL-WENO. Through digital simulation of a linear advection equation, we analyse pros and cons for each method. In order to compare performance, we introduce accuracy computing and Error functions. The accuracy computing is used well-known $L^1-norm$ and the Error functions are dispersion function, dissipation function and total error function. High-order methods well apply to computer simulation, unfortunately, side-effects (Oscillation) happen.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.33 no.5
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• pp.373-379
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• 2020

In this study, TiN-coated cBN (cubic-structure boron nitride) powders were successfully synthesized by a sol-gel method using titanium (IV) isopropoxide (TTIP) and by controlling the heat treatment conditions. After the sol-gel process, amorphous nano-sized TiO_x was uniformly coated on the surface of cBN powder particles. The obtained TiO_x-coated cBN powders were heated at 1,000~1,300℃ for 1 or 6 h in a flow of 95%N₂-5%H₂ mixed gas. With increasing temperature, the chemical composition of the TiO_x coating layer changed in the order of TiO₂→Ti₆O₁₁→Ti₄O₇→TiN due to reduction of the Ti ions. The TiN coating layer was observable in the samples heated at 1,200℃ and appeared as the main phase in the sample heated at 1,300℃. The resulting thickness of the TiN coating layer of the sample heated at 1,300℃ was approximately 45~50 nm.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.45 no.3
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• pp.226-232
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• 2017

Surface pressure distributions over the RAE-A wing-body configuration were investigated and the grid convergence along the streamwise, spanwise, and circumferential directions was numerically studied. Flow analysis in subsonic and transonic conditions was conducted using the $k-{\omega}$ Wilcox-Durbin+ turbulence model. Surface pressure distributions for subsonic flows were well matched, but those for transonic shocked flows showed a little discrepancy with the experimental data. A cubic spline extrapolation method was applied in order to investigate the grid convergence. This method presented that the grid resolution in the circumferential direction is the most important grid parameter. A refined grid system was made based on the grid convergence study and provided more accurate prediction, especially on the symmetric body surface of RAE-A configuration.