Sliding Technique
Ignacio Ruiz, M. Zeron · 2021
This chapter presents the Sliding Technique, yet another technique to sidestep the curse of dimensionality that affects the function-approximating techniques. A slide is an approximating object built in such a way that several of these can be put together to form a larger approximating object. A Chebyshev Slider is a collection of slides built to approximate a function f with the following two conditions: the first is that each of the variables in the domain of f is part of the domain of one and only one slide, and the second is that all slides share the same pivot point. One way of increasing the accuracy of the slider without increasing the number of evaluations relates to the choice of variables that define each slide. Using a slider, one can capture part of the information missed by Taylor approximation.