Approximation of Multivariate Functions
نویسندگان
چکیده
| In this paper, a new class of higher-order feedforward neural networks, called ridge polynomial networks (RPN) is formulated. The new networks are shown to uniformly approximate any continuous function on a compact set in multidimensional input space with any degree of accuracy. Moreover, these networks have an eecient and regular architecture as compared to ordinary higher-order feedforward networks. The RPNs use a special form of ridge polynomials. It is shown that any multivariate polynomial can be represented in terms of this ridge polynomial, and realized by an RPN. The RPN is a generalization of the pi-sigma network which provides a natural mechanism for incremental network growth. Simulation results are provided to show the approximation capability of an incremental learning algorithm for the RPNs.
منابع مشابه
Verification of an Evolutionary-based Wavelet Neural Network Model for Nonlinear Function Approximation
Nonlinear function approximation is one of the most important tasks in system analysis and identification. Several models have been presented to achieve an accurate approximation on nonlinear mathematics functions. However, the majority of the models are specific to certain problems and systems. In this paper, an evolutionary-based wavelet neural network model is proposed for structure definiti...
متن کاملAPPROXIMATION OF 3D-PARAMETRIC FUNCTIONS BY BICUBIC B-SPLINE FUNCTIONS
In this paper we propose a method to approximate a parametric 3 D-function by bicubic B-spline functions
متن کاملFuzzy Best Simultaneous Approximation of a Finite Numbers of Functions
Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.
متن کاملSUPER- AND SUB-ADDITIVE ENVELOPES OF AGGREGATION FUNCTIONS: INTERPLAY BETWEEN LOCAL AND GLOBAL PROPERTIES, AND APPROXIMATION
Super- and sub-additive transformations of aggregation functions have been recently introduced by Greco, Mesiar, Rindone and v{S}ipeky [The superadditive and the subadditive transformations of integrals and aggregation functions, {it Fuzzy Sets and Systems} {bf 291} (2016), 40--53]. In this article we give a survey of the recent development regarding the existence of aggregation functions with ...
متن کاملA continuous approximation fitting to the discrete distributions using ODE
The probability density functions fitting to the discrete probability functions has always been needed, and very important. This paper is fitting the continuous curves which are probability density functions to the binomial probability functions, negative binomial geometrics, poisson and hypergeometric. The main key in these fittings is the use of the derivative concept and common differential ...
متن کامل