Issue No. 12 - December (1991 vol. 40)

ISSN: 0018-9340

pp: 1337-1346

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.106219

ABSTRACT

<p>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.</p>

INDEX TERMS

three dimensional structured networks; matrix equation solving; linear equations; Lyapunov equation; equation-solving problem; pattern array; linear neurons; training algorithms; Lyapunov methods; matrix algebra; neural nets.

CITATION

J.M. Mendel, L.-X. Wang, "Three-Dimensional Structured Networks for Matrix Equation Solving",

*IEEE Transactions on Computers*, vol. 40, no. , pp. 1337-1346, December 1991, doi:10.1109/12.106219