Neural Networks for Solving Systems of Linear Equations and Related Problems

Andrzej Cichock, D. Rolf Unbehauen

Research output: Contribution to journalArticlepeer-review

139 Citations (Scopus)


In this paper various circuit architectures of simple neuron-like analog processors are considered for on-line solving of a system of linear equations with real constant and/or time-variable coefficients. The proposed circuit structures can be used, after slight modifications, in related problems, namely, inversion and pseudo-inversion of matrices and for solving linear and quadratic programming problems. Various ordinary differential equation formulation schemes (generally nonlinear) and corresponding circuit architectures are investigated to find which are best suited for VLSI implementations. Special emphasis is given to ill-conditioned problems. The properties and performance of the proposed circuit structures are investigated by extensive computer simulations.

Original languageEnglish
Pages (from-to)124-138
Number of pages15
JournalIEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Issue number2
Publication statusPublished - Feb 1992
Externally publishedYes


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