• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.479-490
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• 2013

In this paper, we investigate a priori error estimates and superconvergence of varitional discretization for nonlinear parabolic optimal control problems with control constraints. The time discretization is based on the backward Euler method. The state and the adjoint state are approximated by piecewise linear functions and the control is not directly discretized. We derive a priori error estimates for the control and superconvergence between the numerical solution and elliptic projection for the state and the adjoint state and present a numerical example for illustrating our theoretical results.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.175-181
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• 2000

The purpose of this to measure, with explicit constants as small as possible, a priori error bounds for approximation by picewise polynomials. These constants play an important role in the numerical verification method of solutions for obstacle problems by using finite element methods .

• 대한수학회지
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• 제38권1호
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• pp.147-162
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• 2001

This paper establishes exponential decay estimates for the solution of a stationary magnetohydrodynamics equations in a semi-infinite pipe flow when homogeneous lateral surface boundary conditions are applied.

• 대한원격탐사학회지
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• 제28권5호
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• pp.549-559
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• 2012

본 연구는 표고자료의 임의지점에서 표면의 형상에 대한 파라미터들을 추정하는 경우, 추정에 적용된 조정계산모델들의 전통계량이 추정결과를 채택 혹은 기각하는데 적용될 수 있는 정도를 비교분석하는 것을 목적으로 한다. 표면 파라미터 추정시 그 추정결과값을 신뢰할 수 있는지에 대한 여부는 일반적으로 표면의 조건, 그리고 적용된 조정계산모델의 유형에 따라 영향을 받을 것으로 예상되지만 이에 대한 체계적이고 구체적인 연구는 아직 미흡한 실정이다. 원시자료가 실제 관측으로부터 취득된 자료인 경우, 그 참값을 알 수 없기 때문에, 조정계산모델들의 적용적합성을 명확히 파악하기 위하여, 본 연구에서는 원시자료를 모의적으로 생성하여 연구를 수행하였다. 모의자료생성은 각 기준면위에 수평면, 경사면, 그리고 곡면을 포함시키고 일정량의 노이즈를 추가함으로써 연구를 수행하였다. 비교 분석은 모의자료의 임의지점에서 추정된 결과값들을 각 조정계산모델별 전통계량과 연계분석함으로써 수행되었다. 실험결과로부터 조정계산모델들의 다양한 표면조건에 따른 추정특성을 파악할 수 있었다.

• 대한수학회보
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• 제61권2호
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• pp.355-379
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• 2024

In this paper, we establish the curvature estimates for a class of curvature equations with general right hand sides depending on the gradient. We show an existence result by using the continuity method based on a priori estimates. We also derive interior curvature bounds for solutions of a class of curvature equations subject to affine Dirichlet data.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1987년도 한국자동제어학술회의논문집(한일합동학술편); 한국과학기술대학, 충남; 16-17 Oct. 1987
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• pp.721-723
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• 1987

An Adaptation algorithm is presented and a convergence criterion is derived for parallel model reference adaptive bilinear systems. The output error converges asymptotically to zero, and the parameter estimates are bounded for stable reference models. The convergence criterion depends only upon the input sequence and a priori estimates of the maximum parameter values.

• Structural Engineering and Mechanics
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• 제22권4호
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• pp.401-418
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• 2006

Solutions to the problems of structural parameter estimation from modal response using leastsquares minimization of force or displacement residuals are generally sensitive to noise in the response measurements. The sensitivity of the parameter estimates is governed by the physical characteristics of the structure and certain features of the noisy measurements. It has been shown that the regularization method can be used to reduce effects of the measurement noise on the estimation error through adding a regularization function to the parameter estimation objective function. In this paper, we adopt the regularization function as the Euclidean norm of the difference between the values of the currently estimated parameters and the a priori parameter estimates. The effect of the regularization function on the outcome of parameter estimation is determined by a regularization factor. Based on a singular value decomposition of the sensitivity matrix of the structural response, it is shown that the optimal regularization factor is obtained by using the maximum singular value of the sensitivity matrix. This selection exhibits the condition where the effect of the a priori estimates on the solutions to the parameter estimation problem is minimal. The performance of the proposed algorithm is investigated in comparison with certain algorithms selected from the literature by using a numerical example.

• East Asian mathematical journal
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• 제26권5호
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• pp.615-626
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• 2010

In this paper, we analyze discontinuous Galerkin methods with penalty terms, namly symmetric interior penalty Galerkin methods, to solve nonlinear parabolic equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ${\ell}^{\infty}$ ($L^2$) error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

• 대한수학회보
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• 제38권1호
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• pp.29-53
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• 2001

This note presents a an indirect adaptive control scheme for first-order continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. The singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That properties is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. A modification scheme based on the achievement of a modified diagonally dominant Sylvester matrix of the parameter estimates is also given as an alternative method. This diagonal dominance is achieved through estimates modification as a way to guarantee the controllability of the modified estimated model when a controllability measure of the ‘a priori’ estimated model fails. In both schemes, the use of a hysteresis switching function for the modification of the estimates is not required to ensure the nonsingularity of the Sylvester matrix of the estimates.

• 응용통계연구
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• 제7권2호
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• pp.131-143
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• 1994

엔트로피와 스타인손실들을 포함한 비대칭 손실함수아래서 포아송 평균이 사전분포 함수를 갖는 경우에서 베이즈적, 경험적 베이즈 추정치들의 집합을 구하였다. 또한 Efron과 Morris의 접근방법에 의하여 앞에서 제안된 추정치와 기존의 추정치들의 상대절약 손실량을 모의실험을 통하여 비교하였다.