A new application of the extended Euclidean algorithm for matrix Padé approximants (Q1112562)

To compute the matrix Padé approximants [cf. \textit{G. A. Baker jun.}, Essentials of Padé approximants (1975; Zbl 0315.41014)] of a formal power series \(S(x)=\sum^{\infty}_{i=0}s_ ix_ i\) whose coefficients \(s_ i\) are square matrices, the extended Euclidean algorithm is suitably modified. The authors present a Pascal procedure which generates the approximants along an anti-diagonal path in the Padé table of S (if they exist) and illustrate their method by numerical examples.