• Interaction and multiscale mechanics
• /
• 제2권3호
• /
• pp.295-319
• /
• 2009

In this work, we discuss a reproducing kernel collocation method (RKCM) for solving $2^{nd}$ order PDE based on strong formulation, where the reproducing kernel shape functions with compact support are used as approximation functions. The method based on strong form collocation avoids the domain integration, and leads to well-conditioned discrete system of equations. We investigate the convergence and the computational complexity for this proposed method. An important result obtained from the analysis is that the degree of basis in the reproducing kernel approximation has to be greater than one for the method to converge. Some numerical experiments are provided to validate the error analysis. The complexity of RKCM is also analyzed, and the complexity comparison with the weak formulation using reproducing kernel approximation is presented.

• 한국지능시스템학회논문지
• /
• 제13권6호
• /
• pp.635-642
• /
• 2003

강화학습은 제어, 스케쥴링 등 많은 응용분야에서 성공적인 학습 결과를 얻었다. 기본적인 강화학습 알고리즘인 Q-Learning, TD(λ), SARSA 등의 학습 속도의 개선과 기억장소 등의 문제를 해결하기 위해서 여러 함수 근사방법(function approximation methods)이 연구되었다. 대부분의 함수 근사 방법들은 가정을 통하여 강화학습의 일부 특성을 제거하고 사전지식과 사전처리가 필요하다. 예로 Fuzzy Q-Learning은 퍼지 변수를 정의하기 위한 사전 처리가 필요하고, 국소 최소 자승법은 훈련 예제집합을 이용한다. 본 논문에서는 온-라인 퍼지 클러스터링을 이용한 함수 근사 방법인 Fuzzy Q-Map을 제안하다. Fuzzy Q-Map은 사전 지식이 최소한으로 주어진 환경에서, 온라인으로 주어지는 상태를 거리에 따른 소속도(membership degree)를 이용하여 분류하고 행동을 예측한다. Fuzzy Q-Map과 다른 함수 근사 방법인 CMAC와 LWR을 마운틴 카 문제에 적용하여 실험 한 결과 Fuzzy Q-Map은 훈련예제를 사용하지 않는 CMAC보다는 빠르게 최고 예측율에 도달하였고, 훈련 예제를 사용한 LWR보다는 낮은 예측율을 보였다.

• 한국멀티미디어학회논문지
• /
• 제6권4호
• /
• pp.698-706
• /
• 2003

The primary goal of surface approximation is to reduce the degree of deviation of the simplified surface from the original surface. However it is difficult to define the metric that can measure the amount of deviation quantitatively. Many of the existing studies analogize it by using the change of the scalar quantity before and after simplification. This approach makes a lot of sense in the point that the local surfaces with small scalar are relatively less important since they make a low impact on the adjacent areas and thus can be removed from the current surface. However using scalar value alone there can exist many cases that cannot compute the degree of geometric importance of local surface. Especially the perceptual geometric features providing important clues to understand an object, in our observation, are generally constructed with small scalar value. This means that the distinguishing features can be removed in the earlier stage of the simplification process. In this paper, to resolve this problem, we present various factors and their combination as the metric for calculating the deviation error by introducing the orientation of local surfaces. Experimental results indicate that the surface orientation has an important influence on measuring deviation error and the proposed combined error metric works well retaining the relatively high curvature regions on the object's surface constructed with various and complex curvatures.

• 호남수학학술지
• /
• 제42권2호
• /
• pp.251-268
• /
• 2020

In this paper, we estimate the degree of approximation by means of the complete modulus of continuity, the partial modulus of continuity, the Lipschitz-type class and Petree's K-functional for the bivariate Szász-Kantorovich operators based on Brenke-type polynomials. Later, we construct Generalized Boolean Sum operators associated with combinations of the Szász-Kantorovich operators based on Brenke-type polynomials. In addition, we obtain the rate of convergence for the GBS operators with the help of the mixed modulus of continuity and the Lipschitz class of the Bögel continuous functions.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1988년도 한국자동제어학술회의논문집(국제학술편); 한국전력공사연수원, 서울; 21-22 Oct. 1988
• /
• pp.934-938
• /
• 1988

In this paper we present a method of determining the unknown degree of any 2D discrete linear shift-invariant system which is characterized only by the coefficients of the double power series of a transfer function, i.e. a 2D impulse response array. Our method is based on a 2D extension of Berlekamp-Massey algorithm for synthesis of linear feedback shift registers, and it gives a novel approach to identification and approximation of 2D linear systems, which can be distinguished in its simplicity and potential of applicability from the other 2D Levinson-type algorithms. Furthermore, we can solve problems of 2D Pade approximation and 2D system reduction on a reasonable assumption in the context of 2D linear systems theory.

• 대한수학회보
• /
• 제52권2호
• /
• pp.593-601
• /
• 2015

Let $f{\in}C^r$ ([-1,1]), $r{\geq}0$ and let $L^*$ be a linear left fractional differential operator such that $L^*$ $(f){\geq}0$ throughout [0, 1]. We can find a sequence of polynomials $Q_n$ of degree ${\leq}n$ such that $L^*$ $(Q_n){\geq}0$ over [0, 1], furthermore f is approximated left fractionally and simulta-neously by $Q_n$ on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for $f^{(r)}$.

• 한국CDE학회논문집
• /
• 제11권1호
• /
• pp.1-10
• /
• 2006

This paper addresses B-spline curve approximation of a set of ordered points to a specified toterance. The important issue in this problem is to reduce the number of control points while keeping the desired accuracy in the resulting B-spline curve. In this paper we propose a new method for error-bounded B-spline curve approximation based on adaptive selection of dominant points. The method first selects from the given points initial dominant points that govern the overall shape of the point set. It then computes a knot vector using the dominant points and performs B-spline curve fitting to all the given points. If the fitted B-spline curve cannot approximate the points within the tolerance, the method selects more points as dominant points and repeats the curve fitting process. The knots are determined in each step by averaging the parameters of the dominant points. The resulting curve is a piecewise B-spline curve of order (degree+1) p with $C^{(p-2)}$ continuity at each knot. The shape index of a point set is introduced to facilitate the dominant point selection during the iterative curve fitting process. Compared with previous methods for error-bounded B-spline curve approximation, the proposed method requires much less control points to approximate the given point set with the desired shape fidelity. Some experimental results demonstrate its usefulness and quality.

• 대한수학회논문집
• /
• 제38권4호
• /
• pp.1127-1139
• /
• 2023

We investigate an extension of Schauder's theorem by studying the relationship between various s-numbers of an operator T and its adjoint T^*. We have three main results. First, we present a new proof that the approximation number of T and T^* are equal for compact operators. Second, for non-compact, bounded linear operators from X to Y, we obtain a relationship between certain s-numbers of T and T^* under natural conditions on X and Y . Lastly, for non-compact operators that are compact with respect to certain approximation schemes, we prove results for comparing the degree of compactness of T with that of its adjoint T^*.

• Journal of Ship and Ocean Technology
• /
• 제8권2호
• /
• pp.41-60
• /
• 2004

Ship design process requires lots of complicated analyses for determining a large number of design variables. Due to its complexity, the process is divided into several tractable designs or analysis problems. The interdependent relationship requires repetitive works. This paper employs collaborative optimization (CO), one of the multidisciplinary design optimization (MDO) techniques, for treating such complex relationship. CO guarantees disciplinary autonomy while maintaining interdisciplinary compatibility due to its bi-level optimization structure. However, the considerably increased computational time and the slow convergence have been reported as its drawbacks. This paper proposes the use of an approximation model in place of the disciplinary optimization in the system-level optimization. Neural network classification is employed as a classifier to determine whether a design point is feasible or not. Kriging is also combined with the classification to make up for the weakness that the classification cannot estimate the degree of infeasibility. For the purpose of enhancing the accuracy of a predicted optimum and reducing the required number of disciplinary optimizations, an approximation management framework is also employed in the system-level optimization.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1988년도 한국자동제어학술회의논문집(국제학술편); 한국전력공사연수원, 서울; 21-22 Oct. 1988
• /
• pp.753-758
• /
• 1988

In this paper, we propose a new method of designing a reduced-order controller for a linear discrete-time system. Firstly, we study a design problem for a two-degree-of-freedom control system with a feedforward controller. Secondly, in order to obtain a reduced-order controller, frequency-weighted least squares approximation problems are considered. Thirdly, we propose a synthesis procedure of a reduced-order controller. Finally, an example is given to illustrate the effectiveness of this proposed method.