• 제목/요약/키워드: approximation function

검색결과 1,091건 처리시간 0.031초

DEGREE OF APPROXIMATION TO A SMOOTH FUNCTION BY GENERALIZED TRANSLATION NETWORKS

  • HAHM, NAHMWOO;YANG, MEEHYEA;HONG, BUM IL
    • 호남수학학술지
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    • 제27권2호
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    • pp.225-232
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    • 2005
  • We obtain the approximation order to a smooth function on a compact subset of $\mathbb{R}$ by generalized translation networks. In our study, the activation function is infinitely many times continuously differentiable function but it does not have special properties around ${\infty}$ and $-{\infty}$ like a sigmoidal activation function. Using the Jackson's Theorem, we get the approximation order. Especially, we obtain the approximation order by a neural network with a fixed threshold.

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OPTIMAL APPROXIMATION BY ONE GAUSSIAN FUNCTION TO PROBABILITY DENSITY FUNCTIONS

  • Gwang Il Kim;Seung Yeon Cho;Doobae Jun
    • East Asian mathematical journal
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    • 제39권5호
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    • pp.537-547
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    • 2023
  • In this paper, we introduce the optimal approximation by a Gaussian function for a probability density function. We show that the approximation can be obtained by solving a non-linear system of parameters of Gaussian function. Then, to understand the non-normality of the empirical distributions observed in financial markets, we consider the nearly Gaussian function that consists of an optimally approximated Gaussian function and a small periodically oscillating density function. We show that, depending on the parameters of the oscillation, the nearly Gaussian functions can have fairly thick heavy tails.

개선된 이점 대각 이차 근사화를 이용한 함수 근사화 (Function Approximation Using an Enhanced Two-Point Diagonal Quadratic Approximation)

  • 김종립;강우진;최동훈
    • 대한기계학회논문집A
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    • 제28권4호
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    • pp.475-480
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    • 2004
  • Function approximation is one of the most important and active research fields in design optimization. Accurate function approximations can reduce the repetitive computational effort fur system analysis. So this study presents an enhanced two-point diagonal quadratic approximation method. The proposed method is based on the Two-point Diagonal Quadratic Approximation method. But unlike TDQA, the suggested method has two quadratic terms, the diagonal term and the correction term. Therefore this method overcomes the disadvantage of TDQA when the derivatives of two design points are same signed values. And in the proposed method, both the approximate function and derivative values at two design points are equal to the exact counterparts whether the signs of derivatives at two design points are the same or not. Several numerical examples are presented to show the merits of the proposed method compared to the other forms used in the literature.

APPROXIMATION ORDER TO A FUNCTION IN $C^1$[0, 1] AND ITS DERIVATIVE BY A FEEDFOWARD NEURAL NETWORK

  • Hahm, Nahm-Woo;Hong, Bum-Il
    • Journal of applied mathematics & informatics
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    • 제27권1_2호
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    • pp.139-147
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    • 2009
  • We study the neural network approximation to a function in $C^1$[0, 1] and its derivative. In [3], we used even trigonometric polynomials in order to get an approximation order to a function in $L_p$ space. In this paper, we show the simultaneous approximation order to a function in $C^1$[0, 1] using a Bernstein polynomial and a feedforward neural network. Our proofs are constructive.

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Approximation for the Two-Dimensional Gaussian Q-Function and Its Applications

  • Park, Jin-Ah;Park, Seung-Keun
    • ETRI Journal
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    • 제32권1호
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    • pp.145-147
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    • 2010
  • In this letter, we present a new approximation for the twodimensional (2-D) Gaussian Q-function. The result is represented by only the one-dimensional (1-D) Gaussian Q-function. Unlike the previous 1-D Gaussian-type approximation, the presented approximation can be applied to compute the 2-D Gaussian Q-function with large correlations.

Accuracy Analysis of Optimal Trajectory Planning Methods Based on Function Approximation for a Four-DOF Biped Walking Model

  • Peng Chunye;ONO Kyosuke
    • Journal of Mechanical Science and Technology
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    • 제19권spc1호
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    • pp.452-460
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    • 2005
  • Based on an introduced optimal trajectory planning method, this paper mainly deals with the accuracy analysis during the function approximation process of the optimal trajectory planning method. The basis functions are composed of Hermit polynomials and Fourier series to improve the approximation accuracy. Since the approximation accuracy is affected by the given orders of each basis function, the accuracy of the optimal solution is examined by changing the combinations of the orders of Hermit polynomials and Fourier series as the approximation basis functions. As a result, it is found that the proper approximation basis functions are the $5^{th}$ order Hermit polynomials and the $7^{th}-10^{th}$ order of Fourier series.

A SIMULTANEOUS NEURAL NETWORK APPROXIMATION WITH THE SQUASHING FUNCTION

  • Hahm, Nahm-Woo;Hong, Bum-Il
    • 호남수학학술지
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    • 제31권2호
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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.

APPROXIMATION ORDER TO A FUNCTION IN Lp SPACE BY GENERALIZED TRANSLATION NETWORKS

  • HAHM, NAHMWOO;HONG, BUM IL
    • 호남수학학술지
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    • 제28권1호
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    • pp.125-133
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    • 2006
  • We investigate the approximation order to a function in $L_p$[-1, 1] for $0{\leq}p<{\infty}$ by generalized translation networks. In most papers related to neural network approximation, sigmoidal functions are adapted as an activation function. In our research, we choose an infinitely many times continuously differentiable function as an activation function. Using the integral modulus of continuity and the divided difference formula, we get the approximation order to a function in $L_p$[-1, 1].

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확장된 근사 알고리즘을 이용한 조합 방법 (Rule of Combination Using Expanded Approximation Algorithm)

  • 문원식
    • 디지털산업정보학회논문지
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    • 제9권3호
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    • pp.21-30
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    • 2013
  • Powell-Miller theory is a good method to express or treat incorrect information. But it has limitation that requires too much time to apply to actual situation because computational complexity increases in exponential and functional way. Accordingly, there have been several attempts to reduce computational complexity but side effect followed - certainty factor fell. This study suggested expanded Approximation Algorithm. Expanded Approximation Algorithm is a method to consider both smallest supersets and largest subsets to expand basic space into a space including inverse set and to reduce Approximation error. By using expanded Approximation Algorithm suggested in the study, basic probability assignment function value of subsets was alloted and added to basic probability assignment function value of sets related to the subsets. This made subsets newly created become Approximation more efficiently. As a result, it could be known that certain function value which is based on basic probability assignment function is closely near actual optimal result. And certainty in correctness can be obtained while computational complexity could be reduced. by using Algorithm suggested in the study, exact information necessary for a system can be obtained.