Abstract

A new nonlinear activation function is formulated to minimize the time taken to converge to the solution of the complex-valued time-varying problems such as matrix inversion, linear equation, Sylvester equation, Lyapunov equation and Moore-Penrose inversion. These problems play a vital role in real-time systems in which decisions are taken based on the solution of the equations. In the case of real-valued problems, numerous nonlinear activation functions were proposed and investigated. The question of convergence becomes difficult when various activation functions are applied to complex-valued problems. The error in the computation process of the problems can be reduced by using monotonically increasing odd activation functions in which the problem is modeled as a complex-valued Zhang neural network. A new nonlinear activation function called Li-hyperbolic sine is proposed. Many other activation functions are applied to test the superior performance of the proposed Li-hyperbolic sine activation function. Theoretical results show the stability of convergence. The network is expanded component-wise using the Kronecker product and solved numerically. Several examples are used to measure the superior convergence of the Li-hyperbolic sine over other activation functions on complex-valued problems.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 1
Year: 2022

DOI: 10.12732/ijam.v35i1.6

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