In this thesis, new fast algorithms for polynomial interpolation and evaluation on the Chebyshev node set are introduced and the computational complexity of these
methods are discussed. We consider polynomial evaluation and interpolation on a set of points, with particular attention to the case of Fourier points (roots of unity).
This case brings us to the Discrete Fourier Transform and to the Fast Fourier Transform algorithms. Then the evaluation-interpolation technique is introduced and is
also applied to the computation of a polynomial product and the evaluation of a polynomial at a shifted variable. In order to make comparisons of these new
algorithms with the standard algorithms (Horner's method and standard polynomial product), Fortran program codes are written for each technique and the results
are discussed at several points. All these work showed that the cost of the new fast algorithms are of O(n log n) arithmetic operations.

Keywords : Chebyshev nodes, Polynomial interpolation, Polynomial evaluation, Algorithms, Computational complexity, Fast Fourier transform.