Simultaneous Frobenius–Padé approximants

In this paper, we extend to simultaneous approximation the notion of Frobenius–Padé approximants; we then construct rational approximants for vector functions given by their expansion in an orthogonal series. After giving the definitions and notations for simultaneous Frobenius–Padé approximants and table, we develop recursive relations for computing different sequences in the table of approximants. We then propose algorithms to compute, in the two dimensional case, antidiagonal (Kronecker type algorithm) and diagonal sequences.