A fast polynomial interpolation for Remez exchange method

The computational complexity of several algorithms for polynomial interpolation is quantitatively evaluated. There are four well-known algorithms for obtaining the interpolation polynomial. The first algorithm is to solve simultaneous equations for coefficients of the polynomial (the most basic one). The second is Lagrange´s interpolation algorithm (the classical one used widely). The third is Lagrange´s algorithm in the barycentric form. The fourth is Newton´s interpolation algorithm (using divided differences). Using Newton´s interpolation in the method, one can make the Remez exchange method faster, which is useful for the design of linear-phase Chebyshev FIR (finite impulse response) digital filters