New methodologies are designed to reduce the time complexity of an implicit discrete-time differentiator and the simulation time to implement it. They rely on Horner's method and the Shaw-Traub algorithm. The algorithms are compared for differentiators of orders 3, 7, and 10. The Half-Horner and Full-Horner methods showed the best performance and time complexity.
Cite
@article{arxiv.2105.00126,
title = {On the Efficient Implementation of an Implicit Discrete-Time Differentiator},
author = {José Eduardo Carvajal-Rubio and Juan Diego Sánchez-Torres and Michael Defoort and Mohamed Djemai and Alexander G. Loukianov},
journal= {arXiv preprint arXiv:2105.00126},
year = {2021}
}