Title :
An optimization network for solving a set of simultaneous linear equations
Author :
Chakraborty, Kanad ; Mehrotta, K. ; Mohan, Chilukuri K. ; Ranka, Sanjay
Author_Institution :
Sch. of Comput. & Inf. Sci., Syracuse Univ., NY, USA
Abstract :
A network for solving systems of simultaneous linear equations based on Hopfield´s neural network model with continuous, real-valued outputs is described. The network is composed of highly interconnected simple neurons with a linear transfer function at each node. It is guaranteed to converge to a correct solution for all solvable systems of equations irrespective of the choice of the node transfer function; the use of complex nonlinearities at the nodes only affects the network convergence time. When a system which admits a solution is given as input, the network converges spontaneously and rapidly to a very accurate solution in all cases. When an unsolvable system is provided as input, the network outputs fail to converge and make the energy function close to zero even after a very large number of iterations
Keywords :
Hopfield neural nets; convergence; linear algebra; Hopfield nets; complex nonlinearities; continuous outputs; energy function; highly interconnected simple neurons; linear transfer function; network convergence time; neural network model; optimization network; real-valued outputs; simultaneous linear equations; Computer networks; Cost function; Design optimization; Equations; Hopfield neural networks; Information science; Neural networks; Neurons; Symmetric matrices; Vectors;
Conference_Titel :
Neural Networks, 1992. IJCNN., International Joint Conference on
Conference_Location :
Baltimore, MD
Print_ISBN :
0-7803-0559-0
DOI :
10.1109/IJCNN.1992.226936
