Rational and generalised rational Chebyshev approximation problems and their applications

In this research, we study rational and generalised rational Chebyshev approximation problems, their extensions, and their applications in different disciplines. Rational approximations are very flexible than other extensively studied approximation classes such as polynomial and piecewise polynomial approximations. This research explores many potential applications of rational functions. Some of them are theoretical, aiming at evaluating matrix functions, while some others are very applied, particularly, in data analysis where raw data are approximated by suitable rational functions to enhance the efficiency. Moreover, rational functions have recently attracted interest due to their potential use as an activation function in neural networks.