A fast polynomial interpolation for Remez exchange method

Abstract

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. >