SPECTRAL METHODS OF POLYNOMIAL INTERPOLATION AND APPROXIMATION

The classical problem of interpolation and approximation of functions by polynomials is considered here as a special case of spectral representation of functions. This approach was previously developed by us for the orthogonal Legendre and Chebyshev polynomials. Here, we use fundamental Newton polynomials as basis functions. It is shown that the spectral approach has computational advantages over the divided difference method. In a number of problems, Newton and Hermite interpolations are indistinguishable with our approach and are calculated using the same formulas. Also, the computational algorithms that we proposed earlier using orthogonal polynomials are transferred without changes to Newton and Hermite polynomials.

spectral methods, Newton and Hermite polynomials, interpolation and approximation