Approximation of an infinitely differentiable function based on the given discrete computational grid,
at intermediate evaluation points. The algorithm implements a more accurate version of the naive
polynomial interpolation, following
the paper Finding the Zeros of a Univariate Equation:
Proxy Rootfinders, Chebyshev Interpolation, and the Companion
Matrix by John P. Boyd.
Made as the Course Project 2 for Numerical Analysis and Scientific Computing-1 (MTH308B).
For functions with insanely large evaluation points, the observed accuracy improved by a factor of 10 trillion as compared to the naive interpolation method, after multiple runs on Matlab 2019a interpreter.
[1] JOHN P. BOYD, Finding the Zeros of a Univariate Equation...
[2] Wikipedia Contributers, Polynomial Interpolation, Wikipedia
Acknowledgment @kpsunil, for referencing the paper and the previous implementation.