• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.477-488
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• 2012

The convergence rate of a numerical procedure based on Schwarz Alternating Method(SAM) for solving elliptic boundary value problems depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It has been observed that the mixed interface condition, controlled by a parameter, can optimize SAM's convergence rate. In [8], one introduced the two-layer multi-parameterized SAM and determined the optimal values of the multi-parameters to produce the best convergence rate for one-dimensional elliptic boundary value problems. In this paper, we present a method which utilizes the one-dimensional result to get the optimal convergence rate for the two-dimensional problem.

• 제어로봇시스템학회논문지
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• 제8권1호
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• pp.60-66
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• 2002

In this paper, a new target pointing guidance algorithm is proposed by combining the optimal target pointing solution and a simple time-to-Go estimator. Also investigated are some properties of the guidance algorithm which include a relation to conventional PNG, convergence region and convergence trajectories of error states according to the time-to-go estimator gain. Some guidelines for designing the pointing guidance law are commented based on the convergence properties. A design example in the case of large initial heading errors is presented and its performance is investigated by simulation.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.161-171
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• 2011

The convergence rate of a numerical procedure based on Schwarz Alternating Method(SAM) for solving elliptic boundary value problems depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It has been observed that the Robin condition (mixed interface condition), controlled by a parameter, can optimize SAM's convergence rate. In [7], one had formulated the multi-parameterized SAM and determined the optimal values of the multi-parameters to produce the best convergence rate for one-dimensional elliptic boundary value problems. However it was not successful for two-dimensional problem. In this paper, we present a new method which utilizes the one-dimensional result to get the optimal convergence rate for the two-dimensional problem.

• Communications for Statistical Applications and Methods
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• 제6권1호
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• pp.53-68
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• 1999

To improve the slow convergence property of the steepest ascent type algorithm for continuous D-optimal design problems. we develop a new algorithm. We apply the nonlinear system of equations as the necessary condition of optimality and develop the two-point algorithm that solves the problem of clustering. Because of the nature of the steepest coordinate ascent algorithm avoiding the problem of clustering itself helps the improvement of convergence speed. The numerical examples show the performances of the new method is better than those of various steepest ascent algorithms.

• Journal of the Korean Statistical Society
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• 제19권2호
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• pp.105-112
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• 1990

Let (X, Y) be a pair random variables and let f denote the regression function of the response Y on the measurement variable X. Let K(f) denote a derivative of f. The least squares method is used to obtain a tensor spline estimator $\hat{f}$ of f based on a random sample of size n from the distribution of (X, Y). Under some mild conditions, it is shown that $K(\hat{f})$ achieves the optimal rate of convergence for the estimation of K(f) in $L_2$ and $L_{\infty}$ norms.

• Journal of applied mathematics & informatics
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• 제5권1호
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• pp.171-180
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• 1998

In this paper we analyze the convergence of the semidis-crete solution of the Roseneau equation. We introduce the auxiliary projection of the solution and derive the optimal convergence of the semidiscrete solution as well as the auxiliary projection in L2 normed space.

• Korean Journal of Mathematics
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• 제6권2호
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• pp.195-203
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• 1998

In [3], we showed that overintegration may be needed to obtain the optimal $H^1$ error rate for the $p$ version. In this paper, we examine the convergence of the $p$ version in practice, and comment on the implementation of the $p$ version in commercial codes. Also, we give an example of a problem with extremely rough coefficients, for which overintegration is necessary to obtain the optimal $H^1$ convergence rate.

• 대한수학회보
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• 제49권4호
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• pp.829-850
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• 2012

In this paper, we adopt symmetric interior penalty discontinuous Galerkin (SIPG) methods to approximate the solution of nonlinear viscoelasticity-type equations. We construct finite element space which consists of piecewise continuous polynomials. We introduce an appropriate elliptic-type projection and prove its approximation properties. We construct semidiscrete discontinuous Galerkin approximations and prove the optimal convergence in $L^2$ normed space.

• 한국산업융합학회 논문집
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• 제24권6_2호
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• pp.891-897
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• 2021

In this paper, we propose a destination optimal route algorithm for providing route finding service for the transportation handicapped by using the multi-criteria decision-making technique and the modified A-STAR optimal route search algorithm. This is a method to set the route to the destination centering on safety by replacing the distance cost of the existing A-STAR optimal route search algorithm with the safety cost calculated through AHP/TOPSIS analysis. To this end, 10 factors such as road damage, curb, and road hole were first classified as poor road factors that hinder road driving, and then pairwise comparison of AHP was analyzed and then defined as the weight of TOPSIS. Afterwards, the degree of driving safety was quantified for a certain road section in Busan through TOPSIS analysis, and the development of an optimal route search algorithm for the transportation handicapped that replaces the distance cost with safety in the finally modified A-STAR optimal route algorithm was completed.

• 대한수학회지
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• 제47권1호
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• pp.83-100
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• 2010

In this article, an optimal control problem associated with convection-diffusion equation is considered. Using Lagrange multiplier, the optimality system is obtained. The derived optimal system becomes coupled, non-symmetric partial differential equations. For discretizations and implementations, the finite element multigrid V-cycle is employed. The convergence analysis of finite element multigrid methods for the derived optimal system is shown. Some numerical simulations are performed.