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Paper details
Number 3 - September 1994
Volume 4 - 1994
Applications of neural-type structured networks for solving algebraic matrix equations and computation of the Drazin inverse
Andrzej Cichocki, Tadeusz Kaczorek
Abstract
An overview of the methods of solving algebraic matrix equations and computation of the Drazin inverse of a singular matrix with the use of neural-type structured networks is presented. Algebraic matrix equations of the form A1XB1 + A2XB2 + ... + AnXBn = C and the algebraic Riccati equation ATX + XA - XWX + Q = 0 with one unknown matrix X and the matrix equations AX - YB = C with two unknown matrices X, Y are considered. An extension for polynomial matrix equations of the form AXB = C is also presented. The presented algorithms are based on the gradient optimization technique and the standard back-propagation learning algorithm.
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