Bi-orthogonality in rational approximation
It is well known that the Padé denominators of a Stieltjes series (a power series whose coefficients are the moments of a positive measure) are linked to orthogonal polynomials with respect to that measure. Rational interpolants of more general type are connected with orthogonal polynomials with respect to other measures. Here the authors show that simultaneous Padé approximants and Levin- Sidi approximants are connected with bi-orthogonal polynomials, polynomials \(p_ n\) which annihilate a collection of measures \(\phi_ m\). In this more general setting it is also sometimes possible to prove results on the zeros of the polynomials and convergence of approximants.
scientific article; zbMATH DE number 4019658
scientific article