• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.141-148
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• 2009

We consider various algorithms calculating best onesided simultaneous approximations. We assume that X is a compact subset of $\mathbb{R}^{m}$ satisfying $X=\overline{intX}$, S is an n-dimensional subspace of C(X), and $\mu$ is any 'admissible' measure on X. For any l-tuple $f_1,\;{\cdots},\;f_{\ell}$ in C(X), we present various ideas for best approximation to F from S(F). The problem of best (both one and two-sided) approximation is a linear programming problem.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.223-232
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• 2022

The purpose of the paper is to define f-projection operator to develop the f-projection method. The existence of a variational inequality problem is studied using fixed point theorem which establishes the existence of f-projection method. The concept of ρ-projective operator and σ-involutory operator are defined with suitable examples. The relation in between ρ-projective operator and σ-involutory operator are shown. The concept of σ-involutory variational inequality problem is defined and its existence theorem is also established.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.705-710
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• 2010

Let $C_1(X)$ be a normed linear space over ${\mathbb{R}}^m$, and S be an n-dimensional subspace of $C_1(X)$ with spaned by {$s_1,{\cdots},s_n$}. For each ${\ell}$- tuple vectors F in $C_1(X)$, the two-sided best simultaneous approximation problem is $$\min_{s{\in}S}\;\max\limits_{i=1}^\ell\{{\parallel}f_i-s{\parallel}_1\}$$. A $s{\in}S$ attaining the above minimum is called a two-sided best simultaneous approximation or a Chebyshev center for $F=\{f_1,{\cdots},f_{\ell}\}$ from S. This paper is concerned with algorithm for calculating two-sided best simultaneous approximation, in the case of continuous functions.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.3
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• pp.105-122
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• 1995

Based on linear models, the inference about the true measurement x$_{f}$ and the optimal designs x (nx1) for the calibration experiments are considered via Baysian statistical decision analysis. The posterior distribution of x$_{f}$ given the observation y$_{f}$ (qxl) and the calibration experiment is obtained with normal priors for x$_{f}$ and for themodel parameters (.alpha., .betha.). This posterior distribution is not in the form of any known distributions, which leads to the use of a numerical integration or an approximation for the calculation of the overall expected loss. The general structure of the expected loss function is characterized in the form of a conjecture. A near-optimal design is obtained through the approximation nof the conditional covariance matrix of the joint distribution of (x$_{f}$ , y$_{f}$ $^{T}$ )$^{T}$ . Numerical results for the univariate case are given to demonstrate the conjecture and to evaluate the approximation.n.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.1
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• pp.47-61
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• 2003

Two principally different statements of the problem of stable numerical differentiation are considered. It is analyzed when it is possible in principle to get a stable approximation to the derivative ${\Large f}'$ given noisy data ${\Large f}_{\delta}$. Computational aspects of the problem are discussed and illustrated by examples. These examples show the practical value of the new understanding of the problem of stable differentiation.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.435-443
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• 2007

An important approach towards solving the scattered data problem is by using radial basis functions. However, for a large class of smooth basis functions such as Gaussians, the existing theories guarantee the interpolant to approximate well only for a very small class of very smooth approximate which is the so-called 'native' space. The approximands f need to be extremely smooth. Hence, the purpose of this paper is to study approximation by a scattered shifts of a radial basis functions. We provide error estimates on larger spaces, especially on the homogeneous Sobolev spaces.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.35-45
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• 2001

In this paper we point out an Ostrowski type inequality for the Riemann-Stieltjes integral ${\int}_a^b$ f (t) du (t), where f is of p-H-$H{\ddot{o}}lder$ type on [a,b], and u is of bounded variation on [a,b]. Applications for the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also given.

• Tribology and Lubricants
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• v.38 no.3
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• pp.84-92
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• 2022

In Part I, developed was a method to obtain the stress field due to an edge dislocation that locates in an elastic half plane beneath the contact edge of an elastically similar square wedge. Essential result was the corrective functions which incorporate a traction free condition of the free surfaces. In the sequel to Part I, features of the corrective functions, F_kij,(k = x, y;i,j = x,y) are investigated in this Part II at first. It is found that F_xxx(ŷ) = F_xyx(ŷ) where ŷ = y/η and η being the location of an edge dislocation on the y axis. When compared with the corrective functions derived for the case of an edge dislocation at x = ξ, analogy is found when the indices of y and x are exchanged with each other as can be readily expected. The corrective functions are curve fitted by using the scatter data generated using a numerical technique. The algebraic form for the curve fitting is designed as F_kij(ŷ) = $\frac{1}{\hat{y}^{1-{\lambda}}I+yp}$$\sum_{q=0}^{m}{\left}$$\left[A_q\left(\frac{\hat{y}}{1+\hat{y}} \right)^q \right]$ where λ_I=0.5445, the eigenvalue of the adhesive complete contact problem introduced in Part I. To investigate the exponent of F_kij, i.e.(1 - λ_I) and p, Log|F_kij|(ŷ)-Log|(ŷ)| is plotted and investigated. All the coefficients and powers in the algebraic form of the corrective functions are obtained using Mathematica. Method of analyzing a surface perpendicular crack emanated from the complete contact edge is explained as an application of the curve-fitted corrective functions.

• Proceedings of the IEEK Conference
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• 2001.06c
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• pp.15-168
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• 2001

In this paper, we propose growing algorithm of wavelet neural network. It is growing algorithm that adds hidden nodes using wavelet frame which approximately supports orthogonality in wavelet neural network based on wavelet theory. The result of this processing can be reduced global error and progresses performance efficiency of wavelet neural network. We apply the proposed algorithm to approximation problem and evaluate effectiveness of proposed algorithm.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.843-859
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• 2000

An Ostrowski type integral inequality for the Riemann-Stieltjes integral ${\int^b}_a$ f(t) du(t), where f is assumed to be of bounded variation on [a, b] and u is of r - H - $H\"{o}lder$ type on the same interval, is given. Applications to the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out.