• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.713-727
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• 2016

In this paper, we introduce two general iteration schemes with bounded error terms and prove some theorems related to the strong and ${\Delta}$-convergence of these iteration schemes for multi-valued maps in a hyperbolic space. The results which are presented here extend and improve some well-known results in the current literature.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.135-154
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• 2018

In this paper, an almost second order overlapping Schwarz method for singularly perturbed third order convection-diffusion type problem is constructed. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the combination of classical finite difference scheme and central finite difference scheme on a uniform mesh while on the non-layer region we use the midpoint difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. We proved that, when appropriate subdomains are used, the method produces convergence of second order. Furthermore, it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantages of this method used with the proposed scheme are it reduce iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.347-350
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• 2004

In this paper, the acceleration is studied for the rigid-plastic FEM of metal forming simulation. In the FEM, the direct iteration and Newton-Raphson iteration are applied to obtain the initial solution and accurate solution respectively. In general, the acceleration scheme for the direct iteration is not used. In this paper, an Aitken accelerator is applied to the direct iteration. In the modified Newton-Raphson iteration, the step length or the deceleration coefficient is used for the fast and robust convergence. The step length can be determined by using the accelerator. The numerical experiments have been performed for the comparisons. The faster convergence is obtained with the acceleration in the direct and Newton-Raphson iterations.

• Honam Mathematical Journal
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• v.38 no.1
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• pp.127-139
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• 2016

In this paper, we construct an iteration scheme involving a hybrid pair of nonexpansive mappings and utilize the same to prove some convergence theorems. In process, we remove a restricted condition (called end-point condition) in Sokhuma and Kaewkhao's results [Sokhuma and Kaewkhao, Fixed Point Theory Appl. 2010, Art. ID 618767, 9 pp.].

• The Journal of Korean Institute of Communications and Information Sciences
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• v.39A no.9
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• pp.566-568
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• 2014

In this letter, an MMSE based iterative soft decision interference cancellation scheme for massive MIMO systems is proposed. To reduce the complexity, the proposed scheme uses the Sherman-Morrison-Woodbury formula to compute the entire MMSE filtering vectors in one iteration by one matrix inverse operation. Simulation results show that the proposed scheme also has a comparable BER to the conventional scheme for massive MIMO systems.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.181-203
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• 2018

In this paper, we have constructed an overlapping Schwarz method for singularly perturbed second order convection-diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the central finite difference scheme on a uniform mesh while on the non-layer region we use the mid-point difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. When appropriate subdomains are used, the numerical approximations generated from the method are shown to be first order convergent. Furthermore it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantages of this method used with the proposed scheme is it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.11
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• pp.1118-1124
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• 2014

This paper proposes a novel controller design scheme for multimachine power systems based on the explorized policy iteration. Power systems have several uncertainties on system dynamics due to the various effects of interconnections between generators. To solve this problem, the proposed method solves the LQR (Linear Quadratic Regulation) problem of isolated subsystems without the knowledge of a system matrix and the interconnection parameters of multimachine power systems. By selecting the proper performance indices, it guarantees the stability and convergence of the LQ optimal control. To implement the proposed scheme, the least squares based online method is also investigated in terms of PE (Persistency of Excitation), interconnection parameters and exploration signals. Finally, the performance and effectiveness of the proposed algorithm are demonstrated by numerical simulations of three-machine power systems with governor controllers.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.235-252
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• 2014

In this paper, weak and strong convergence theorems of three step iteration process with errors are established for two weakly inward and non-self asymptotically nonexpansive mappings in Banach spaces. The results obtained in this paper extend and improve the several recent results in this area.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.243-248
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• 1997

A full multigrid scheme was used in computing some eigenvalues of the Laplace eigenvalues problem with the Dirichlet bound-ary condition. We get a system of algebraic equations with an aid of finite difference method and apply subspace iteration method to the system to compute first some eigenvalues. The result shows that this is very effective in calculating some eigenvalues of this problem.

• The Pure and Applied Mathematics
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• v.11 no.4
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• pp.337-348
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• 2004

In this paper, we suggest and analyze Noor (three-step) iterative scheme for solving nonlinear strongly accretive operator equation Tχ = f. The results obtained in this paper represent an extension as well as refinement of previous known results.