• Journal of Institute of Control, Robotics and Systems
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• v.15 no.11
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• pp.1137-1143
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• 2009

This paper presents the FPGA implementation of efficient algorithms for approximating exponential function based on floating point format data. The Taylor-Maclaurin expansion as a conventional approximation method becomes inefficient since high order expansion is required for the large number to satisfy the approximation error. A format converter is designed to convert fixed data format to floating data format, and then the real number is separated into two fields, an integer field and an exponent field to separately perform mathematic operations. A new assembly command is designed and added to previously developed command set to refer the math table. To test the proposed algorithm, assembly program has been developed. The program is downloaded into the Altera DSP KIT W/STRATIX II EP2S180N Board. Performances of the proposed method are compared with those of the Taylor-Maclaurin expansion.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.29A no.2
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• pp.1-7
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• 1992

A consideration for image improvement under the Born approximation in the microwave diffraction tomography is suggested by using a projection function. The limiting factors in the degrading reconstructed image due to Born approximation are identified in terms of projection function and its modification is suggested to improve the degraded image based upon the Born approximation. In order to verify the proposed method, the reconstructed images are shown by computer simulation from the back-scattered data of angular and frequency diversity for squared dielectric cylinder with a various relative dielectric constant. From simulation results, it was shown that the proposed method can lead to a fairly good improved image for a severe degraded one irrespective of homogeneous and inhomogeneous dielectric object. In the future, the analysis on the limitation of this method should be considered and performed by means of more quantitative method.

• The Korean Journal of Applied Statistics
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• v.11 no.2
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• pp.287-302
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• 1998

Saddlepoint approximation to the distribution function of sample mean(Daniels, 1987) is extended to the case of general statistic in this paper. The suggested approximation methods are applied to derive the approximations to the distributions of some statistics, including sample valiance and studentized mean. Some comparisons with other methods show that the suggested approximations are very accurate for moderate or small sample sizes. Even in extreme tail the accuracies are also maintained.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.279-287
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• 2003

In this paper we propose a local smoothing of the Nelson type estimator for the survival function based on an approximation by the Weibull distribution function. It appears that Mean Square Error and Bias of the smoothed estimator of the Nelson type survival function estimators are significantly smaller than that of the smoothed estimator of the Kaplan-Meier survival function estimator.

• 한국데이터정보과학회:학술대회논문집
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• 2003.05a
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• pp.109-119
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• 2003

In this paper we propose a local smoothing of the Nelson type estimator for the survival function based on an approximation by the Weibull distribution function. It appears that Mean Square Error and Bias of the smoothed estimator of the Nelson type survival function estimator is significantly smaller then that of the smoothed estimator of the Kaplan-Meier survival function estimator.

• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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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.

• ETRI Journal
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• v.15 no.2
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• pp.35-51
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• 1993

This paper presents function approximation based on nonparametric estimation. As an estimation model of function approximation, a three layered network composed of input, hidden and output layers is considered. The input and output layers have linear activation units while the hidden layer has nonlinear activation units or kernel functions which have the characteristics of bounds and locality. Using this type of network, a many-to-one function is synthesized over the domain of the input space by a number of kernel functions. In this network, we have to estimate the necessary number of kernel functions as well as the parameters associated with kernel functions. For this purpose, a new method of parameter estimation in which linear learning rule is applied between hidden and output layers while nonlinear (piecewise-linear) learning rule is applied between input and hidden layers, is considered. The linear learning rule updates the output weights between hidden and output layers based on the Linear Minimization of Mean Square Error (LMMSE) sense in the space of kernel functions while the nonlinear learning rule updates the parameters of kernel functions based on the gradient of the actual output of network with respect to the parameters (especially, the shape) of kernel functions. This approach of parameter adaptation provides near optimal values of the parameters associated with kernel functions in the sense of minimizing mean square error. As a result, the suggested nonparametric estimation provides an efficient way of function approximation from the view point of the number of kernel functions as well as learning speed.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.5
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• pp.397-404
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• 2002

In this paper, it is proposed wavelet neural network using the fuzzy concept with the fuzzy and the multi-resolution analysis(MRA) of wavelet transform. Also, it wishes to improve any nonlinear function learning approximation using this system. Here, the fuzzy concept is used the bell type fuzzy membership function. And the composition of wavelet has a unit size. It is used the backpropagation algorithm for learning of wavelet neural network using the fuzzy concept. It is used the multi-resolution analysis of wavelet transform, the bell type fuzzy membership function and the backpropagation algorithm for learning. This structure is confirmed to be improved approximation performance than the conventional algorithms from one dimension and two dimensions function through simulation.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.741-754
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• 2002

In this paper we present an error bound for cubic spline approximation of conic section curve. We compare it to the error bound proposed by Floater [1]. The error estimating function proposed in this paper is sharper than Floater's at the mid-point of parameter, which means the overall error bound is sharper than Floater's if the estimating function has the maximum at the midpoint.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.729-738
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• 2013

In this paper, we investigate a localized approximation of a continuously differentiable function by neural networks. To do this, we first approximate a continuously differentiable function by B-spline functions and then approximate B-spline functions by neural networks. Our proofs are constructive and we give numerical results to support our theory.