Approximations for nonlinear functions

Author

Sandberg, Irwin W.

Author_Institution

Dept. of Electr. & Comput. Eng., Texas Univ., Austin, TX, USA

Volume

39

Issue

1

fYear

1992

fDate

1/1/1992 12:00:00 AM

Firstpage

65

Lastpage

67

Abstract

Results concerning the uniform approximation of nonlinear functionals on compact sets are discussed. The results are of interest in connection with neural network-like classifiers for continuous-time signals and approximations for the input-output maps of dynamic systems. It is shown that function-space feedforward neural networks with one input layer of bounded linear functionals and one hidden nonlinear layer each are universal approximators of real continuous functionals on compact subsets of a normed linear space

Keywords

function approximation; neural nets; bounded linear functionals; compact sets; continuous-time signals; dynamic systems; function-space feedforward neural networks; hidden nonlinear layer; input-output maps; neural network-like classifiers; nonlinear functions; normed linear space; real continuous functionals; Circuits; Eigenvalues and eigenfunctions; Feedback; Feedforward neural networks; Jacobian matrices; Linear systems; Neural networks; Nonlinear equations; Polynomials; Software packages;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.109247

Filename

109247