Title :
Global asymptotic convergence of nonlinear relaxation equations realised through a recurrent perceptron
Author :
Mandic, Danilo P. ; Chambers, Jonathon A.
Author_Institution :
Dept. of Electr. & Electron. Eng., Imperial Coll. of Sci., Technol. & Med., London, UK
Abstract :
Conditions for global asymptotic stability (GAS) of a nonlinear relaxation equation realised by a nonlinear autoregressive moving average (NARMA) recurrent perceptron are provided. Convergence is derived through fixed point iteration (FPI) techniques, based upon a contraction mapping feature of a nonlinear activation function of a neuron. Furthermore, nesting is shown to be a spatial interpretation of an FPI, which underpins a pipelined recurrent neural network (PRNN) for nonlinear signal processing
Keywords :
asymptotic stability; autoregressive moving average processes; fixed point arithmetic; iterative methods; nonlinear equations; numerical stability; perceptrons; recurrent neural nets; signal processing; FPI technique; GAS; NARMA; PRNN; contraction mapping feature; convergence; fixed point iteration; global asymptotic convergence; nonlinear activation function; nonlinear autoregressive moving average recurrent perceptron; nonlinear relaxation equations; nonlinear signal processing; pipelined recurrent neural network; recurrent perceptron; spatial interpretation; Asymptotic stability; Convergence; Linear systems; Logistics; Neurons; Nonlinear equations; Pipeline processing; Recurrent neural networks; Signal processing; Vectors;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1999. Proceedings., 1999 IEEE International Conference on
Conference_Location :
Phoenix, AZ
Print_ISBN :
0-7803-5041-3
DOI :
10.1109/ICASSP.1999.759885
