Row Convergence Theorems for Vector-Valued Padé Approximants Original Research Article

Yet another method of proof of de Montessusʹ 1902 theorem is given. We show how this proof readily extends to row convergence theorems for four different kinds of vector Padé approximants. These approximants all belong to the category associated with vector-valuedC-fractions formed using generalised inverses. The proof of a conjecture by Graves-Morris and Saff (J. Comput. Appl. Math.23, 1988, 63–85) is given and new row convergence theorems for hybrid vector Padé approximants are proved.