Cyclic AFD algorithm for the 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 and on the real line. The type of approximation is proved to be equivalent with Blaschke form approximation. The algorithm is called Cyclic adaptive Fourier decomposition as it adaptively selects one parameter for each cycle on the basis of the maximal selection principle proved in the literature of adaptive Fourier decomposition. Copyright © 2013 John Wiley & Sons, Ltd.