Convergence analysis of an augmented algorithm for fully complex-valued neural networks

This paper presents an augmented algorithm for fully complex-valued neural network based on Wirtinger calculus, which simplifies the derivation of the algorithm and eliminates the Schwarz symmetry restriction on the activation functions. A unified mean value theorem is first established for general functions of complex variables, covering the analytic functions, non-analytic functions and real-valued functions. Based on so introduced theorem, convergence results of the augmented algorithm are obtained under mild conditions. Simulations are provided to support the analysis. (C) 2015 Elsevier Ltd. All rights reserved.