• Honam Mathematical Journal
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• v.31 no.2
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• pp.147-156
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• 2009

In this paper, we actually construct the simultaneous approximation by neural networks to a differentiable function. To do this, we first construct a polynomial approximation using the Fejer sum and then a simultaneous neural network approximation with the squashing activation function. We also give numerical results to support our theory.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.713-719
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• 2011

The problem of approximation from a set of scattered data arises in a wide range of applied mathematics and scientific applications. In this study, we present a quasi-interpolatory approximation scheme for scattered data approximation problem, which reproduces a certain space of polynomials. The proposed scheme is local in the sense that for an evaluation point, the contribution of a data value to the approximating value is decreasing rapidly as the distance between two data points is increasing.

• The Journal of the Acoustical Society of Korea
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• v.24 no.1
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• pp.1-10
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• 2005

This paper presents a wideband LPA (local polynomial approximation) beamforming algorithm that is appropriate for wideband moving sources. The Proposed wideband LPA algorithm adopts STMV (steered minimum variance) method that utilizes a steered covariance matrix obtained from multiple frequency components in one data snapshot, instead of multiple data snapshots in one frequency bin. The wideband LPA cost function is formed using STMV weight vector. The Proposed algorithm searches for the instantaneous DOA and angular velocity that maximize the wideband LPA cost function. resulting in a higher resolution performance than that of a DS LPA beamforming algorithm. Several simulations using artificial data and sea trial data are used to demonstrate the performance of the Proposed algorithm.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.287-292
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• 2005

This paper presents a rational polynomial approximation method to estimate modal parameters of wind excited structures using incomplete noisy measurements of structural responses and partial measurements of wind velocities only. A stochastic model of the excitation wind force acting on the structure is estimated from partial measurements of wind velocities. Then the transfer functions of the structure are approximated as rational polynomial functions. From the poles and zeros of the estimated rational polynomial functions, the modal parameters, such as natural frequencies, damping ratios, and mode shapes are extracted. Since the frequency characteristics of wind forces acting on structures can be assumed as a smooth Gaussian process especially around the natural frequencies of the structures according to the central limit theorem (Brillinger, 1969; Yaglom, 1987), the estimated modal parameters are robust and reliable with respect to the assumed stochastic input models. To verify the proposed method, the modal parameters of a TV transmission tower excited by gust wind are estimated. Comparison study with the results of other researchers shows the efficacy of the suggested method.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2002.10a
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• pp.376-380
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• 2002

This research presents modeling of a functional surface which is a constructed free-formed surface. The modeling introduced in this paper adopts polynomial regression that is utilizing approximating technique. The measured data are obtained from measuring with Coordinate Measuring Machine. This paper introduces efficient methods of Reverse Engineering using Polynomial Regression.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.42-47
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• 2001

Analyzing the ECG signal, we can find heart disease, for example, arrhythmia and myocardial infarction, etc. Particularly, detecting arrhythmia is more important, because serious arrhythmia can take away the life from patients within ten minutes. In this paper, we would like to introduce the signal processing for ECG analysis and the device made for wireless communication of ECG data. In the signal processing, the wavelet transform decomposes the ECG signal into high and low frequency components using wavelet function. Recomposing the high frequency bands including QRS complex, we can detect QRS complex and eliminate the noise from the original ECG signal. To recognize the ECG signal pattern, we adopted the polynomial approximation partially and statistical method. The ECG signal is divided into small parts based on QRS complex, and then, each part is approximated to the polynomials. Comparing the approximated ECG pattern with the database, we can detect and classify the heart disease. The ECG detection device consists of amplifier, filters, A/D converter and RF module. After amplification and filtering, the ECG signal is fed through the A/D converter to be digitalized. The digital ECG data is transmitted to the personal computer through the RF transceiver module and serial port.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.7
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• pp.1315-1320
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• 2007

In this paper, we introduce a new fuzzy model called fuzzy combined polynomial neural networks, which are based on the representative fuzzy model named polynomial fuzzy model. In the design procedure of the proposed fuzzy model, the coefficients on consequent parts are estimated by using not general least square estimation algorithm that is a sort of global learning algorithm but weighted least square estimation algorithm, a sort of local learning algorithm. We are able to adopt various type of structures as the consequent part of fuzzy model when using a local learning algorithm. Among various structures, we select Polynomial Neural Networks which have nonlinear characteristic and the final result of which is a complex mathematical polynomial. The approximation ability of the proposed model can be improved using Polynomial Neural Networks as the consequent part.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.4
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• pp.280-286
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• 1987

A new method is presented for obtaining redced-order model for time-invariant systems. This method does not require the calculation of the reciprocal transformation, the alpha table, the beta-table and the alpha-beta expansion which should be calculated in Routh approximation method, hence it is computationally very attractive better than Routh approximation method, furthemore the stability of the reduced-order model is guaranted if the original system is stable. This method starts with the continued fraction espansion of auxiliary denominator polynomial give for the denominator polynomial of the reduced-order model. The coefficients of the numerator polynomial are then obtained by equating moment of the original and the reduced-order medel.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.756-761
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• 2004

The effects of two important numerical procedures on the high precision structural analysis are investigated in this study. The two numerical procedures include continuous variable approximation and time integration. For the continuous variable approximation, polynomial mode functions generated by the Gram-Schmidt process are introduced and the numerical results obtained by employing the polynomial mode functions are compared to those obtained by classical beam mode functions. The effect of the time integration procedure on the analysis precision is also investigated. It is found that the two procedures affect the precision of structural analysis significantly.

• Journal of information and communication convergence engineering
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• v.6 no.3
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• pp.320-322
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• 2008

We present efficient algorithms for solving the piecewise-cubic approximation problems in the plane. Given a set D of n points in the plane, we find a piecewise-cubic polynomial curve passing through only the points of a subset S of D and approximating the other points using the uniform metric. The goal is to minimize the size of S for a given error tolerance $\varepsilon$, called the min-# problem, or to minimize the error tolerance $\varepsilon$ for a given size of S, called the min-$\varepsilon$ problem. We give algorithms with running times O($n^2$ logn) and O($n^3$) for both problems, respectively.