Three-dimensional structured networks for matrix equation solving

Author

Wang, Li Xin ; Mendel, Jerry M.

Author_Institution

Dept. of Electr. Eng.-Syst., Univ. of Southern California, Los Angeles, CA, USA

Volume

40

Issue

12

fYear

1991

fDate

12/1/1991 12:00:00 AM

Firstpage

1337

Lastpage

1346

Abstract

Two three-dimensional structured networks are developed for solving linear equations and the Lyapunov equation. The basic idea of the structured network approaches is to first represent a given equation-solving problem by a 3-D structured network so that if the network matches a desired pattern array, the weights of the linear neurons give the solution to the problem: then, train the 3-D structured network to match the desired pattern array using some training algorithms; and finally, obtain the solution to the specific problem from the converged weights of the network. The training algorithms for the two 3-D structured networks are proved to converge exponentially fast to the correct solutions. Simulations were performed to show the detailed convergence behaviors of the 3-D structured networks

Keywords

Lyapunov methods; matrix algebra; neural nets; Lyapunov equation; equation-solving problem; linear equations; linear neurons; matrix equation solving; pattern array; three dimensional structured networks; training algorithms; Algorithm design and analysis; Artificial neural networks; Convergence; Equations; Feedforward neural networks; Matrices; Neural networks; Neurons; Parallel processing; Pattern matching;

fLanguage

English

Journal_Title

Computers, IEEE Transactions on

Publisher

ieee

ISSN

0018-9340

Type

jour

DOI

10.1109/12.106219

Filename

106219