Cyclic AFD algorithm for best rational approximation

We propose a practical algorithm of best rational approximation of a given order to a function in the Hardy H2 space on the unit circle or on the real line. The type approximation is proved to be equivalent with Blaschke form approximation. The algorithm is called Cyclic AFD as it adaptively selects one parameter during each cycle based on the Maximal Selection Principle used in adaptive Fourier decomposition (AFD)