Title :
Approximations for nonlinear functions
Author :
Sandberg, Irwin W.
Author_Institution :
Dept. of Electr. & Comput. Eng., Texas Univ., Austin, TX, USA
fDate :
1/1/1992 12:00:00 AM
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;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
