Continuity of approximation by least-squares multivariate Padé approximants
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.
scientific article; zbMATH DE number 1423322