• Journal of Applied and Pure Mathematics
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• 제4권3_4호
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• pp.185-209
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• 2022

Here we exhibit multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝ^N, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the generalized symmetrical sigmoid function. The approximations are point-wise and uniform. The related feed-forward neural network is with one hidden layer.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.567-584
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• 2014

In this paper, we consider approximation of eigenelements of a two dimensional compact integral operator with a smooth kernel by discrete collocation and iterated discrete collocation methods. By choosing numerical quadrature appropriately, we obtain convergence rates for gap between the spectral subspaces, and also we obtain superconvergence rates for eigenvalues and iterated eigenvectors. We then apply Richardson extrapolation to obtain further improved error bounds for the eigenvalues. Numerical examples are presented to illustrate theoretical estimates.

• Journal of Applied and Pure Mathematics
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• 제5권1_2호
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• pp.69-93
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• 2023

Here we give multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝ^N, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by a parametrized Gudermannian sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer.

• 산업경영시스템학회지
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• 제36권4호
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• pp.77-83
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• 2013

This study is to develop a mathematical analysis model to grasp the behaviors of cartels. Cartels are formed tacitly and cause tremendous damage to consumers in modern society which is composed of advanced industry structure. The government authorities have instituted the leniency programs to respond cartels. However, cartels will continue unless there are legal sanctions against cartels based on an accurate analysis of leniency programs. The proposed cartel equilibrium analysis model is a mathematical behavior model which is based on the existing methods and the prison's dilemma of game theory. Therefore, the model has a form of pay off matrix of two players. We use a iterated polymatrix approximation (IPA) method to deduct a Nash equilibrium point. The model is validated by an empirical analysis as well.

• 대한수학회논문집
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• 제37권3호
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• pp.765-800
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• 2022

Quantization for probability distributions concerns the best approximation of a d-dimensional probability distribution P by a discrete probability with a given number n of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on ℝ. For such a probability measure P, an induction formula to determine the optimal sets of n-means and the nth quantization error for every natural number n is given. In addition, using the induction formula we give some results and observations about the optimal sets of n-means for all n ≥ 2.

• 대한전자공학회논문지SP
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• 제41권3호
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• pp.121-127
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• 2004

This paper presents a new vertex selection scheme for shape approximation. In the proposed method, final vertex points are determined by "two-step procedure". In the first step, initial vertices are simply selected on the contour, which constitute a subset of the original contour, using conventional methods such as an iterated refinement method (IRM) or a progressive vertex selection (PVS) method In the second step, a vertex adjustment Process is incorporated to generate final vertices which are no more confined to the contour and optimal in the view of the given distortion measure. For the optimality of the final vertices, the dynamic programming (DP)-based solution for the adjustment of vertices is proposed. There are two main contributions of this work First, we show that DP can be successfully applied to vertex adjustment. Second, by using DP, the global optimality in the vertex selection can be achieved without iterative processes. Experimental results are presented to show the superiority of our method over the traditional methods.

• 대한전기학회논문지:전기물성ㆍ응용부문C
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• 제49권11호
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• pp.616-621
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• 2000

This paper deals with the multiresolution analysis of wavelet transform for partial discharge(PD). Test arrangement is based on the needle-plane electrode system and applied AC high voltage. The measured PD signal was decomposed into "approximations" and "details". The approximation are the high scale, low-frequency components of the PD signal. The details are the low-scale, high frequency components. The decomposition process are iterated to 3 level, with successive approximation being decomposed in turn, so that PD signal is broken down into many lower-resolution components. Through the procedure of signal wavelet transform, signal noise extraction and signal reconstruction, the signal is analyzed to determine the magnitude of PD.

• 대한전자공학회논문지SP
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• 제40권1호
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• pp.114-123
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• 2003

본 논문에서는 영상 객체 (object) 의 모양 정보를 효율적으로 부호화 하는 기법을 제안한다. 다각 근사화 기법은 손실 부호화 기법으로써 객체의 모양을 근사화 하는데 가장 널리 사용되고 있다. 제안된 기법은 최대 허용 오차를 만족하면서 정점을 선택할 때 기존의 순환 정점 선택 (IRM: iterated refinement method) 이나 순차적 정점 선택 (PVS: progressive vertex selection) 보다 적은 수의 정점을 선택함으로써 비트량을 줄인다. 기존의 순차적인 정점 선택 기법을 기반으로 하여 새로운 정점 선택 조건을 제안하여 비트량-왜곡면에서 우수한 성능을 가지는 부호화기를 구현하였다. 실험 결과에서 제안된 기법이 기존의 정점 선택 기법들에 비해 우수한 성능을 나타냄을 알 수 있다.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.41-60
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• 2000

In this paper we consider a series of algorithms for calculating radicals of matrix polynomial equations. A particular aspect of this problem arise in author's work. concerning parameter identification of linear dynamic stochastic system. Special attention is given of searching the solution of an equation in a neighbourhood of some initial approximation. The offered approaches and algorithms allow us to receive fast and quite exact solution. We give some recommendations for application of given algorithms.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2005년도 춘계학술대회 논문집
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• pp.1040-1044
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• 2005

This paper presents a method for the robot localization and calibration using the ultrasonic and the radio frequency. The distance between the receiver and a beacon can be computed by using the difference between times of flight. The presented method uses the gradient of the maximum amplitude of the ultrasonic in order to measure the time of flight precisely. The measured three distances between the receiver and the beacon are used to compute the robot position by the direct inverse method and the iterated least square approximation method. This paper is defined the calibration as the problem to find the location of 3 beacons and 3 robots, and presents 3 methods for it and found the 2B2R method as the best among them.