Rectangular matrix Padé approximants and square matrix orthogonal polynomials
Using the method of linear functionals introduced by \textit{C. Brezinski} [Padé-type approximation and general orthogonal polynomials (1980; Zbl 0418.41012] the authors study rectangular (left) matrix Padé approximants to formal power series with \(p\times q\) matrices as coefficients. The parallel to the classical scalar case is remarkable. Existence and uniqueness can be ascertained using (generalized) Hankel determinants, recurrence relations along a diagonal in the Padé table are given, a matrix \(qd\)-algorithm is derived. Classical results are also extended to generalized square matrix orthogonal polynomials and their associated polynomials with respect to the linear functional. Finally the connection between right and left matrix Padé approximant is studied. The resuts show that the method originally introduced for the scalar case (Brezinski loc. cit.) extends in a natural way to the much more intricate situation of non-square matrix approximants.
rectangular matrix Padé-type approximant
scientific article; zbMATH DE number 1078342