• International Journal of CAD/CAM
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• 제13권1호
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• pp.1-11
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• 2013

Just by adjusting the control points iteratively, progressive iterative approximation (PIA) presents an intuitive and straightforward scheme such that the resulting limit curve (surface) can interpolate the original data points. In order to obtain more flexibility, adjusting only a subset of the control points, a new method called local progressive iterative approximation (LPIA) has also been proposed. But to this day, there are two problems about PIA and LPIA: (1) Only an approximation process is discussed, but the accurate convergence curves (surfaces) are not given. (2) In order to obtain an interpolating curve (surface) with high accuracy, recursion computations are needed time after time, which result in a large workload. To overcome these limitations, this paper gives an explicit matrix expression of the control points of the limit curve (surface) by the PIA or LPIA method, and proves that the column vector consisting of the control points of the PIA's limit curve (or surface) can be obtained by multiplying the column vector consisting of the original data points on the left by the inverse matrix of the collocation matrix (or the Kronecker product of the collocation matrices in two direction) of the blending basis at the parametric values chosen by the original data points. Analogously, the control points of the LPIA's limit curve (or surface) can also be calculated by one-step. Furthermore, the $G^1$ joining conditions between two adjacent limit curves obtained from two neighboring data points sets are derived. Finally, a simple LPIA method is given to make the given tangential conditions at the endpoints can be satisfied by the limit curve.

• East Asian mathematical journal
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• 제28권5호
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• pp.617-630
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• 2012

In this paper, the problem of iterative approximation of common fixed points of asymptotically nonexpansive is investigated in the framework of Banach spaces. Weak convergence theorems are established. A necessary and sufficient condition for strong convergence is also discussed. As an application of main results, a variational inequality is investigated.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1233-1245
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• 2008

In this paper, an iterative method is proposed to solve the least-squares problem of matrix equation AXB+CYD=E over unknown matrix pair [X, Y]. By this iterative method, for any initial matrix pair [$X_1,\;Y_1$], a solution pair or the least-norm least-squares solution pair of which can be obtained within finite iterative steps in the absence of roundoff errors. In addition, we also consider the optimal approximation problem for the given matrix pair [$X_0,\;Y_0$] in Frobenius norm. Given numerical examples show that the algorithm is efficient.

• Korean Journal of Mathematics
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• 제4권2호
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• pp.83-88
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• 1996

In 1994 Z.Liang constructed an iterative method for the solution of nonlinear equations involving m-accretive operators in uniformly smooth Banach spaces. In this paper we apply the slight variants of Liang's iterative methods and generalize the results of Z.Liang. Moreover our proof is more simple than Liang's proof.

• 대한수학회지
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• 제46권1호
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• pp.83-97
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• 2009

Two new iterative algorithms are provided to find zeros of accretive operators in a Banach space E with a uniformly $G\hat{a}teaux$ differentiable norm. Strong convergence for two iterations is proved and as applications, the viscosity approximation results are obtained also.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 학술대회 논문집 정보 및 제어부문
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• pp.723-725
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• 2004

An iterative robust control design for PZT using Gaussian wavelet networks is proposed. A Gaussian wavelet network with accurate approximation capability is employed to approximate the nonlinear hysteresis dynamics of PZT systems by using an iterative control algorithm. Depending on the finite number of wavelet basis functions which results in unavoidable approximation errors, a robust control law is provided to guarantee the stability of the closed-loop nano positioning system. Finally, the effectiveness of the robust control approach is illustrated through comparative simulations on a PZT.

• 한국정밀공학회지
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• 제20권6호
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• pp.62-70
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• 2003

This paper deals with a approximation and tracking control of hydraulic servo system using a real time recurrent neural networks (RTRN) with 2-dimensional iterative learning rule. And it was driven that 2-dimensional iterative learning rule in discrete time. In order to control the trajectory of position, two RTRN with same network architecture were used. Simulation results show that two RTRN using 2-D learning algorithm is able to approximate the plant output and desired trajectory to a very high degree of a accuracy respectively and the control algorithm using two same RTRN was very effective to control trajectory tracking of electro-hydraulic servo system.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1061-1071
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• 2009

For real generalized reflexive matrices R, S, i.e., $R^T$ = R, $R^2$ = I, $S^T$ = S, $S^2$ = I, we say that real matrix X is (R,S)-symmetric, if RXS = X. In this paper, an iterative algorithm is proposed to solve the least-squares problem of matrix equation AXB = C with (R,S)-symmetric X. Furthermore, the optimal approximation solution to given matrix $X_0$ is also derived by this iterative algorithm. Finally, given numerical example and its convergent curve show that this method is feasible and efficient.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 봄 학술발표회 논문집
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• pp.275-283
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• 2004

The paper describes the integrated design system using MDO and approximation technique. In MDO related research, final target is an integrated and automated MDO framework systems. However, in order to construct the integrated design system, the prerequisite condition is how much save computational cost because of iterative process in optimization design and lots of data information in CAD/CAE integration. Therefore, this paper presents that an efficient approximation method, Adaptive Approximation, is a competent strategy via MDO framework systems.

• 대한수학회보
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• 제38권2호
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• pp.293-302
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• 2001

We improve the greedy algorithm which is one of the general convergence criterion for certain iterative sequence in a given space by building a constructive greedy algorithm on a normed linear space using an arithmetic average of elements. We also show the degree of approximation order is still $Ο(1\sqrt{\n}$) by a bounded linear functional defined on a bounded subset of a normed linear space which offers a good approximation method for neural networks.