Padé and Rational approximation, Theory and Applications location:Amsterdan, The Netherlands date:29-31 October 1980
The solution of the trigonometric moment problem involves the computation of a (0/n) Laurent-Padé approximant for a positive real function on the complex unit circle. The incoming scheme is equivalent to the recursion for Szegö's orthogonal polynomials, while the outgoing scheme is equivalent to the Schur recursion for contractions of the unit disc. The numerical stability of both algorithms is proved under certain conditions via a backward error analysis.
Padé Approximation and its Applications, Amsterdam 1980