“…Rational approximation is an old subject, and many algorithms have been proposed over the years. Probably nobody has a complete view of this terrain, as the developments have occurred in diverse fields including often highly theoretical approximation theory [3,4,16,30,47,48,50,54,55,56,57,60,61], physics [6,29,31,32,33], systems and control [1,2,9,20,22,24,36,37,38,42,49,52], extrapolation of sequences and series [17,18,19], and numerical linear algebra [10,39,43]. The languages and emphases differ widely among the fields, with the systems and control literature, for example, giving particular attention to vector and matrix approximation problems and to approximation on the imaginary axis.…”