Algorithms for solving Hermite interpolation problems using the Fast Fourier Transform

We present a method for computing the Hermite interpolation polynomial based on equally spaced nodes on the unit circle with an arbitrary number of derivatives in the case of algebraic and Laurent polynomials. It is an adaptation of the method of the Fast Fourier Transform (FFT) for this type of problems with the following characteristics: easy computation, small number of operations and easy implementation. second part of the paper we adapt the algorithm for computing the Hermite interpolation polynomial based on the nodes of the Tchebycheff polynomials and we also study Hermite trigonometric interpolation problems.