Continuity of approximation by least-squares multivariate Padé approximants (Q1971831)

The least-squares multivariate Padé approximants (LSPA) are the multivariate approximants with coefficients defined by minimizing a weighted least-square form. The authors prove that if a family of meromorphic functions \(u_h\) (\(h\) is a parameter tending to zero) converges to a meromorphic function \(u\), then the LSPA to \(u_h\) with fixed degree of denominator converges also to \(u\). This property allows to apply the LSPA to approximate the solution of partial differential equations problems depending on some parameters.