• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.8
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• pp.584-593
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• 1987

A new combined approximation method using Routh stability array and mean-square error (MSE) method is proposed for deriving reduced-order z-transter functions for discrete time systems. The Routh stability array is used to obtain the reduced-order denominator polynomial, and the numerator polynomial is obtained by minimizing the mean-square error between the unit step responses of the original system and reduced model. The advantages of the new combined approximation method are that the reduced model is always stable provided the original model is stable and the initial and steady-state characteristics of the original model can be preserved in the reduced model.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.3
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• pp.145-156
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• 2000

In this paper, we propose a new methodology which includes the optimal design procedure of Polynomial Neural Networks(PNN) structure for model identification of complex and nonlinear system. The proposed PNN algorithm is based on GMDA(Group Method of Data handling) method and its structure is similar to Neural Networks. But the structure of PNN is not fixed like in conventional Neural Networks and can be generated. The each node of PNN structure uses several types of high-order polynomial such as linear, quadratic and cubic, and is connected as various kinds of multi-variable inputs. In other words, the PNN uses high-order polynomial as extended type besides quadratic polynomial used in GMDH, and the number of input of its node in each layer depends on that of variables used in the polynomial. The design procedure to obtain an optimal model structure utilizing PNN algorithm is shown in each stage. The study is illustrated with the aid of pH neutralization process data besides representative time series data for gas furnace process used widely for performance comparison, and shows that the proposed PNN algorithm can produce the model with higher accuracy than previous other works. And performance index related to approximation and prediction capabilities of model is evaluated and also discussed.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.493-502
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• 2017

We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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• pp.130-133
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• 2000

In this paper, a new design methodology named FNNN(Fuzzy Polynomial Neural Network) algorithm is proposed to identify the structure and parameters of fuzzy model using PNN(Polynomial Neural Network) structure and a fuzzy inference method. The PNN is the extended structure of the GMDH(Group Method of Data Handling), and uses several types of polynomials such as linear, quadratic and modified quadratic besides the biquadratic polynomial used in the GMDH. The premise of fuzzy inference rules defines by triangular and gaussian type membership function. The fuzzy inference method uses simplified and regression polynomial inference method which is based on the consequence of fuzzy rule expressed with a polynomial such as linear, quadratic and modified quadratic equation are used. Each node of the FPNN is defined as fuzzy rules and its structure is a kind of neuro-fuzzy architecture Several numerical example are used to evaluate the performance of out proposed model. Also we used the training data and testing data set to obtain a balance between the approximation and generalization of proposed model.

• Journal of applied mathematics & informatics
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• v.7 no.1
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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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.88-93
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• 1998

It is frequently important to approximate a rational B$\acute{e}$zier curve by an integral, i.e., polynomial one. This need will arise when a rational B$\acute{e}$zier curve is produced in one CAD system and is to be imported into another system, which can only handle polynomial curves. The objective of this paper is to present an algorithm to approximate rational B$\acute{e}$zier curves with polynomial curves of higher degree.

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.583-592
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• 2007

Given the moments of a symmetric random variable, its density and distribution functions can be accurately approximated by making use of the algorithm proposed in this paper. This algorithm is specially designed for approximating symmetric distributions and comprises of four phases. This approach is essentially based on the transformation of variable technique and moment-based density approximants expressed in terms of the product of an appropriate initial approximant and a polynomial adjustment. Probabilistic quantities such as percentage points and percentiles can also be accurately determined from approximation of the corresponding distribution functions. This algorithm is not only conceptually simple but also easy to implement. As illustrated by the first two numerical examples, the density functions so obtained are in good agreement with the exact values. Moreover, the proposed approximation algorithm can provide the more accurate quantities than direct approximation as shown in the last example.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.1
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• pp.22-32
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• 2024

In this paper we present a method of conic section approximation by hexic Bézier curves. The hexic Bézier approximants are G³ Hermite interpolations of conic sections. We show that there exists at least one hexic Bézier approximant for each weight of the conic section The hexic Bézier approximant depends one parameter and it can be obtained by solving a quartic polynomial, which is solvable algebraically. We present the explicit upper bound of the Hausdorff distance between the conic section and the hexic Bézier approximant. We also prove that our approximation method has the maximal order of approximation. The numerical examples for conic section approximation by hexic Bézier curves are given and illustrate our assertions.

• Journal of Korea Spatial Information System Society
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• v.7 no.2 s.14
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• pp.57-66
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• 2005

The Interconnecting Highways problem is an abstract of many practical Layout Design problems in the areas of VLSI design, the optical and wired network design, and the planning for the road constructions. For the road constructions, the shortest-length road layouts that interconnect existing positions will provide many more economic benefits than others. That is, finding new road layouts to interconnect existing roads and cities over a wide area is an important issue. This paper addresses an approximation scheme that finds near optimal road layouts for the Interconnecting Highways problem which is NP-hard. As long as computational resources are provided, the near optimality can be acquired asymptotically. This implies that the result of the scheme can be regarded as the optimal solution for the problem in practice. While other approximation schemes can be made for the problem, this proposed scheme provides a big merit that the algorithm designed by this scheme fits well to given problem instances.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.176-180
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• 2004

The ST-segment that the beginning part of T wave is the important diagnostic parameter to finding myocardial ischemia. Abnormal ST appears in two types. One is the level change, and the other is the pattern change. In this paper, we describe the monitoring of abnormal ST using PC based system. Hardware of this system consists of transmitter, receiver and PC. The function of transmitter is measuring ECG in three channels which are selected manually and transmitting the data to receiver by digital radio way. Connection with receiver and PC is by RS232C, and the data received on the PC is analyzed automatically by ECG analysis algorithm and saved to file. In the algorithm part for detecting abnormal ST, ST-segments are approximated by a polynomial. This method can detect all of the deviation and pattern change of ST-segment regardless the change in the heart rate or sampling rate. To gain algorithm reliability, the method rejects distorted polynomial approximation by calculation the difference between the approximated ST-segment and original ST-segment. In pre-signal processing, the wavelet transformation separates high frequency bands including QRS complex from the original ECG. Consequently, the process improves the performance of detecting each feature points.