• Journal of the Institute of Electronics Engineers of Korea SD
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• v.40 no.5
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• pp.298-311
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• 2003

Iterative Fourier transform algorithm, (IFTA) is tile iterative numerical algorithm for the design of the diffractive optical elements (DOE), by which the phase distribution of a DOE converges on a local optimal solution. The convergence of IFTA depends on several factors 3s initial phase distribution, the structure of the degree of freedom on the observation plane, and the values of internal parameters. In this paper, we analyze tile dependence of the convergence of IFTA on an internal parameter of IFTA, the relaxation parameter, and propose a new hybrid scheme of genetic algorithm and IFTA to obtain more accurate solution.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.453-465
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• 2000

In this paper, a new method for finding the approximate solution of a second order nonlinear partial differential equation is introduced. In this method the problem is transformed to an equivalent optimization problem. them , by considering it as a distributed parameter control system the theory of measure is used for obtaining the approximate solution of the original problem.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.143-153
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• 2000

In [8], Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we propose the block diagonal preconditioners. The preconditioned conjugate residual method is robust in that the convergence is uniform as the parameter, v, goes to $\sfrac{1}{2}$. Computational experiments are included.

• Journal of the Korean Operations Research and Management Science Society
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• v.7 no.1
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• pp.11-16
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• 1982

A method is described for the solution of a linearly constrained program with parametric nonlinear objective function. The algorithm proposed in this paper may be regarded as an extension of the simplex method for parametric linear programming. Namely, it specifies the basis at each stage such that feasibility ana optimality of the original problem are satisfied by the optimal solution of the reduced parametric problem involving only nonbasic variables. It is shown that under appropriate assumptions the algorithm is finite. Parametric procedures are also indicated for solving each reduced parametric problem by maintaining the Kuhn-Tucker conditions as the parameter value varies.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.41-60
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• 2000

In this paper we consider a series of algorithms for calculating radicals of matrix polynomial equations. A particular aspect of this problem arise in author's work. concerning parameter identification of linear dynamic stochastic system. Special attention is given of searching the solution of an equation in a neighbourhood of some initial approximation. The offered approaches and algorithms allow us to receive fast and quite exact solution. We give some recommendations for application of given algorithms.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.621-632
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• 2014

In this paper, we study the dynamical behavior of the one-dimensional convective Cahn-Hilliard equation(CCHE) on a periodic cell [$-{\pi},{\pi}$]. We prove that as the control parameter passes through the critical number, the CCHE bifurcates from the trivial solution to an attractor. We describe the bifurcated attractor in detail which gives the final patterns of solutions near the trivial solution.

• Journal of the Korean Statistical Society
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• v.33 no.4
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• pp.459-470
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• 2004

We study the approximation of the solution of linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion with Hurst parameter H > 1/2 through discretization of space and time. The rate of convergence of an approximation for Euler scheme is established.

• Journal of Biomedical Engineering Research
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• v.12 no.3
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• pp.171-176
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• 1991

A solution for the course of the general deterministic epidemic model is obtained by elementary series expansion. This is valid over all times, and appears to hold accurate]y over a very wide range of population and threshould parameter values. This algorithm can be more efficient than either numerical or recursive procedures in terms of the number of operations required to evaluate a sequence of points along the course of the epidemic.

• East Asian mathematical journal
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• v.14 no.2
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• pp.399-410
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• 1998

In [3], Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated-linear systems. In this work, we present computational experiments of W-cycle multigrid method. Computational experiments show that the convergence is uniform as the parameter, $\nu$, goes to 1/2.

• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.329-342
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• 2002

We deal with asymptotic properties of Maximum Likelihood Estimator(MLE) for the parameters appearing in a Hilbert space-valued Stochastic Differential Equation(SDE) and a Stochastic Partial Differential Equation(SPDE). In paractice, the available data are only the finite dimensional projections to the solution of the equation. Using these data we obtain MLE and consider the asymptotic properties as the dimension of projections increases. In particular we explore a relationship between the conditions for the solution and asymptotic properties of MLE.