• 호남수학학술지
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• 제35권3호
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• pp.417-433
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• 2013

We consider the iterative solution of a quadratic matrix equation with special coefficient matrices which arises in the quasibirth and death problem. In this paper, we show that the elementwise minimal positive solvent of the quadratic matrix equations can be obtained using Newton's method if there exists a positive solvent and the convergence rate of the Newton iteration is quadratic if the Fr$\acute{e}$chet derivative at the elementwise minimal positive solvent is nonsingular. Although the Fr$\acute{e}$chet derivative is singular, the convergence rate is at least linear. Numerical experiments of the convergence rate are given.

• 전자공학회논문지B
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• 제33B권11호
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• pp.159-166
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• 1996

In this paper, the method for improving the speed of convergence and learning rate of back propagation algorithms is proposed which update the learning rate parameter and momentum term for each weight by generated error, changely the output layer of neural network generates a high value in the case that output value is far from the desired values, and genrates a low value in the opposite case this method decreases the iteration number and is able to learning effectively. The effectiveness of proposed method is verified through the simulation of X-OR and 3-parity problem.

• 대한기계학회논문집B
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• 제22권6호
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• pp.788-802
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• 1998

A numerical method using dual time stepping and preconditioning procedure for efficient computations of unsteady low speed compressible flow problems is developed. The time-derivative preconditioning method which is valid at low speed flow conditions cannot maintain temporal accuracy because of the modification of the time-derivative term in Navier-Stokes equations. The dual time stepping procedure is incorporated to enable the time accurate computations and this procedure introduces a pseudo-time derivative in addition to the physical time derivative. At a given physical time, an inner iteration can be carried out until a steady state in pseudo-time is achieved. This will effectively yield a time accurate solution. Computational capabilities of the above algorithm are demonstrated through computation of a variety of practical fluid flows and it is shown that the algorithms is efficient in the essentially incompressible flows and low Mach number compressible flows with heat source.

• 한국유체기계학회 논문집
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• 제5권3호
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• pp.25-32
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• 2002

Structural and dynamic analyses of inducer and impeller for an oxidizer turbopump are peformed to investigate the safety level of strength and vibration at a design point. Due to high rotational speed of turbopump, effects of centrifugal forces are carefully considered in the structural analysis. Hydrodynamic pressure is also considered as an external force applied to inducer and impeller blades. A three-dimensional Finite Element Method (FEM) is used for linear and nonlinear structural analyses with modified Newton-Raphson iteration method. After the nonlinear trim solution is obtained from the structural analysis, dynamic characteristics are obtained as a function of rotational speed from the linearized eigenvalue analysis at an equilibrium position. According to the results of numerical analysis, the safety margins of strength and vibration resonances are sufficient enough for safe operation within the requited life cycle.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1511-1523
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• 2011

In this paper, we consider the smoothing Newton method for the nonlinear complementarity problems with $P_0$-function. The proposed algorithm is based on a new smoothing function and it needs only to solve one linear system of equations and perform one line search per iteration. Under the condition that the solution set is nonempty and bounded, the proposed algorithm is proved to be convergent globally. Furthermore, the local superlinearly(quadratic) convergence is established under suitable conditions. Preliminary numerical results show that the proposed algorithm is very promising.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1081-1096
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• 2011

In this paper, a steady axisymmetric MHD flow of two dimensional incompressible fluids is studied under the influence of a uniform transverse magnetic field. The governing equations are reduced to nonlinear boundary value problem by applying the integribility conditions. Optimal Homotopy Asymptotic Method (OHAM) is applied to obtain solution of reduced fourth order nonlinear boundary value problem. For comparison, the same problem is also solved by Variational Iteration Method (VIM).

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.233-243
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• 2009

This paper concerns an algorithm that combines line search and trust region step for nonlinear optimization problems. Unlike traditional trust region methods, we incorporate the Armijo line search technique into trust region method to solve the subproblem. In addition, the subproblem is solved accurately, but instead solved by inaccurate method. If a trial step is not accepted, our algorithm performs the Armijo line search from the failed point to find a suitable steplength. At each iteration, the subproblem is solved only one time. In contrast to interior methods, the optimal solution is derived by iterating from outside of the feasible region. In numerical experiment, we apply the algorithm to nonlinear portfolio optimization problems, primary numerical results are presented.

• 한국전산유체공학회지
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• 제8권3호
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• pp.12-20
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• 2003

A numerical procedure for the calculation of solidification and melting phase change using PISO algorithm is presented. In case of phase change problem, the coupling between velocity/pressure/temperature and liquid fraction is important. The converged temperature and liquid fraction solution which satisfies the energy balance is acquired by applying enthalpy method into inner iteration in matrix solver. And a modified PISO algorithm version is introduced to properly solve the coupling between velocity/pressure/temperature and liquid fraction. A comparison of the proposed procedure with a standard iterative method shows improvement both in terms of computing speed and robustness.

• 한국공작기계학회논문집
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• 제12권2호
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• pp.9-16
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• 2003

A strategy of the optimal shape design with FEA(Finite Element Analysis) for 2-D structure is proposed by comparing subproblem approximation method with first order approximation method. A cantilever beam with two different loading conditions, a concentrated load and an evenly distribute load, and truss structure with a concentrated loading condition are implemented to optimize the shape. It gives a good design strategy on the optimal truss structure as well as the optimal cantilever beam shape. It is found that the convergence is quickly finished with the iteration number below ten. Optimized shapes of cantilever beam and truss structure are shown with stress contour plot by the results of the subproblem approximation method and the first order approximation methd.

• Journal of the Korean Statistical Society
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• 제29권3호
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• pp.297-306
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• 2000

An efficient method of constructing $textsc{k}$-minimal path sets to evaluate the reliability of a flow network is presented. The network is considered to be in a functioning state if it can transmit a maximum flow which is greater than or equal to a specified amount of flow, $textsc{k}$say, and a $textsc{k}$-minimal path set is a minimal set of branches that satisfies the given flow constraint. In this paper, under the assumption that minimal path sets of the network are known, we generate composite paths by adding only a minimal set of branches at each iteration to get $textsc{k}$-minimal path sets after possibly the fewest composition, and compute maximum flow of composite paths using only minimal path sets. Thereby we greatly reduce the possible occurrence of redundant composite paths throughout the process and efficiently compute the maximum flow of composite paths generated. Numerical examples illustrate the method.