RT Journal Article
T1 Numerical Implementation of Gradient Algorithms
A1 Atencia-Ruiz, Miguel Alejandro
A1 Hernández, Yadira
A1 Joya-Caparrós, Gonzalo
A1 Sandoval-Hernández, Francisco
K1 Algoritmos computacionales
AB A numerical method for computational implementation of gradient dynamical systems is presented. The method is based upon the development of geometric integration numerical methods, which aim at preserving the dynamical properties of the original ordinary differentialequation under discretization. In particular, the proposed method belongs to the class of discrete gradients methods, which substitute the gradient of the continuous equation with a discrete gradient, leading to a map that possesses the same Lyapunov function of the dynamical system,thus preserving the qualitative properties regardless of the step size. In this work, we apply a discrete gradient method to the implementation of Hopfield neural networks. Contrary to most geometric integrationmethods, the proposed algorithm can be rewritten in explicit form, which considerably improves its performance and stability. Simulation results show that the preservation of the Lyapunov function leads to an improved performance, compared to the conventional discretization.
PB Springer
YR 2013
FD 2013
LK http://hdl.handle.net/10630/5594
UL http://hdl.handle.net/10630/5594
LA eng
NO The final publication is available at link.springer.com. doi:10.1007/978-3-642-38682-4_38
NO Spanish Government project no. TIN2010-16556   Junta de Andalucía project no. P08-TIC-04026    Agencia Española de Cooperación Internacionalpara el Desarrollo project no. A2/038418/11
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026