Recurrent neural networks for solving matrix algebra problems
Author
Živković, Ivan S.Mentor
Stanimirović, Predrag
Committee members
Milovanović, Gradimir
Todorović, Branimir
Janković, Dragan
Petković, Marko
Metadata
Show full item recordAbstract
The aim of this dissertation is the application of recurrent neural
networks (RNNs) to solving some problems from a matrix algebra
with particular reference to the computations of the generalized
inverses as well as solving the matrix equations of constant (timeinvariant)
matrices. We examine the ability to exploit the correlation
between the dynamic state equations of recurrent neural networks for
computing generalized inverses and integral representations of these
generalized inverses. Recurrent neural networks are composed of
independent parts (sub-networks). These sub-networks can work
simultaneously, so parallel and distributed processing can be
accomplished. In this way, the computational advantages over the
existing sequential algorithms can be attained in real-time
applications. We investigate and exploit an analogy between the
scaled hyperpower family (SHPI family) of iterative methods for
computing the matrix inverse and the discretization of Zhang Neural
Netwo...rk (ZNN) models. A class of ZNN models corresponding to the
family of hyperpower iterative methods for computing the generalized
inverses on the basis of the discovered analogy is defined. The Matlab
Simulink implementation of the introduced ZNN models is described
in the case of scaled hyperpower methods of the order 2 and 3. We
present the Matlab Simulink model of a hybrid recursive neural
implicit dynamics and give a simulation and comparison to the
existing Zhang dynamics for real-time matrix inversion. Simulation
results confirm a superior convergence of the hybrid model compared
to Zhang model.