• Journal of Digital Convergence
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• v.12 no.7
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• pp.65-76
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• 2014

This paper analyzes whether local public expenditures have converged during the 1985-2011 periods in Korea, using the sixteen metropolitan and provincial governments data. We analyze the convergence of per capita real local public expenditures in terms of both static view and dynamic view of convergence. Furthermore, we derive the estimating equation for per capita real local government expenditure growth function from theoretical model based on Skidmore et al.(2004)[23]. The main results from empirical analyses are such that an increase in aged people helped local government expenditures increase. Also, we found that the convergence speed of economic expenditure is greater than that of social welfare expenditure. Similarly the convergence speed of public capital expenditure is greater than that of public consumption expenditure. In the future we had better examine the convergence of local public goods taking into account their congestion rates.

• 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 the Korea Convergence Society
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• v.7 no.4
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• pp.217-227
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• 2016

This paper analyzes whether social welfare services converge across the regions. We tested whether local social welfare services converge considering the congestion rate of local social welfare services during the 1985-2013 periods in Korea, using the sixteen higher level local governments panel data. The main findings are as follows. First, the absolute level of local social welfare services converge so that the -convergence exists. Second, the growth rate of local social welfare services increases as the intial level of local social welfare services is lower so that there exists -convergence. The policy implications of our findings are as follows. The local government had better consider the presence of local social welfare services in policy decision making. Also, fundamentally the social welfare policies had better be executed by the central government rather than local governments, since the national minimum welfare must be provided.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1009-1023
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• 2022

The main objective of this work is to investigate the study of the local and semi-local convergence of the contraharmonic-mean Newton's method (CHMN) for solving nonlinear equations in a Banach space. We have performed the semi-local convergence analysis by using generalized conditions. We examine the theoretical results by comparing the CHN method with the Newton's method and other third order methods by Weerakoon et al. using some test functions. The theoretical and numerical results are also supported by the basins of attraction for a selected test function.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.12
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• pp.1210-1218
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• 2011

GA (Genetic Algorithms) are efficient for searching for global optima but may have some problems such as premature convergence, convergence to local extremum and divergence. These phenomena are related to the evolutionary operators. As population diversity converges to low value, the search ability of a GA decreases and premature convergence or converging to local extremum may occur but population diversity converges to high value, then genetic algorithm may diverge. To guarantee that genetic algorithms converge to the global optima, the genetic operators should be chosen properly. In this paper, we analyze the effects of the selection operator, crossover operator, and mutation operator on convergence properties, and propose the sweeping method of mutation probability and elitist propagation rate to maintain the diversity of the GA's population for getting out of the premature convergence. Results of simulation studies verify the feasibility of using these sweeping operators to avoid premature convergence and convergence to local extrema.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.261-267
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• 2006

A local convergence analysis of Newton's method for perturbed generalized equations is provided in a Banach space setting. Using center Lipschitzian conditions which are actually needed instead of Lipschitzian hypotheses on the $Fr\'{e}chet$-derivative of the operator involved and more precise estimates under less computational cost we provide a finer convergence analysis of Newton's method than before [5]-[7].

• 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.

• 한국전산유체공학회:학술대회논문집
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• 2009.04a
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• pp.269-276
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• 2009

The local preconditioning method has both robust convergence and accurate solutions by using local flow properties for parameters in the preconditioning matrix. Preconditioning methods have been very effective to low speed inviscid flows. In the viscous and turbulent flows, deterioration of convergence should be overcame on the high aspect ratio grids to get better convergence and accuracy. In the present study, the local time stepping and min-CFL/max-VNN definitions are applied to compare the results and we propose the method that switches between two methods. The min-CFL definition is applied for inviscid flow problems and the min-CFL/max-VNN definition is implemented to viscous and turbulent flow problems.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.1-12
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• 2015

We present a local convergence analysis for inexact Newton-like method in a Banach space under weaker Lipschitz condition. The convergence ball is enlarged and the estimates on the error distances are more precise under the same computational cost as in earlier studies such as [6, 7, 11, 18]. Some special cases are considered and applications for solving nonlinear systems using the Newton-arithmetic mean method are improved with the new convergence technique.