• 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].

• 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].

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.685-696
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• 1999

We present local and semilocal convergence results for New-ton's method in a Banach space setting. In particular using Lipschitz-type assumptions on the second Frechet-derivative we find results con-cerning the radius of convergence of Newton's method. Such results are useful in the context of predictor-corrector continuation procedures. Finally we provide numerical examples to show that our results can ap-ply where earlier ones using Lipschitz assumption on the first Frechet-derivative fail.

• The Pure and Applied Mathematics
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• v.18 no.3
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• pp.219-230
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• 2011

We determine the radius of convergence for some Newton{type methods (NTM) for approximating a locally unique solution of an equation in a Banach space setting. A comparison is given between the radii of (NTM) and Newton's method (NM). Numerical examples further validating the theoretical results are also provided in this study.

• Journal of Korea Multimedia Society
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• v.20 no.12
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• pp.1951-1959
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• 2017

Due to the fact that 3D printing is applied to many areas of life, 3D printing models are often used illegally without any permission from the original providers. This paper presents a novel watermarking algorithm for the copyright protection and ownership identification for 3D printing based on the radius curvature of 3D triangle. 3D triangles are extracted and classified into groups based on radius curvature by the clustering algorithm, and then the mean radius curvature of each group will be computed for watermark embedding. The watermark data is embedded to the groups of 3D triangle by changing the mean radius curvature of each group. In each group, we select a 3D triangle which has the nearest radius curvature with the changed mean radius curvature. Finally, we change the vertices of the selected facet according to the changed radius curvature has been embedded watermark. In experiments, the distance error between the original 3D printing model and the watermarked 3D printing model is approximate zero, and the Bit Error Rate is also very low. From experimental results, we verify that the proposed algorithm is invisible and robustness with geometric attacks rotation, scaling and translation.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.47-55
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• 2008

Local convergence results for three Newton-like methods in Banach space are provided. A comparison is given between the three convergence radii. Then we show that using the largest convergence radius we can pick an initial guess from with we start the corresponding iteration. It turns out that after a finite number of steps we can always use the iterate found as the starting guess for a faster method, since this iterate will be inside the convergence domain of the new method.

• East Asian mathematical journal
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• v.26 no.3
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• pp.365-370
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• 2010

A local convergence result is provided for the continuous analog of Newton's method in a Banach space setting. The radius of convergence is larger, the error bounds tighter, and under the same or weaker hypotheses than before [12].

• East Asian mathematical journal
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• v.25 no.4
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• pp.425-431
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• 2009

We provide a local convergence analysis for Newton-like methods for the solution of generalized equations in a Banach space setting. Using some ideas of ours introduced in [2] for nonlinear equations we show that under weaker hypotheses and computational cost than in [7] a larger convergence radius and finer error bounds on the distances involved can be obtained.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.41-50
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• 2002

We provide local and semilocal theorems for the convergence of Newton-like methods to a locally unique solution of an equation in a Banach space. The analytic property of the operator involved replaces the usual domain condition for Newton-like methods. In the case of the local results we show that the radius of convergence can be enlarged. A numerical example is given to justify our claim . This observation is important and finds applications in steplength selection in predictor-corrector continuation procedures.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.621-629
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• 2019

In this paper, we present a local convergence analysis of a three point method with convergence order $1.839{\ldots}$ for approximating a locally unique solution of a nonlinear operator equation in setting of Banach spaces. Using weaker hypotheses than in earlier studies, we obtain: larger radius of convergence and more precise error estimates on the distances involved. Finally, numerical examples are used to show the advantages of the main results over earlier results.