Error formulas for multivariate rational interpolation and Pade´approximation

Error formulas for multivariate rational interpolation and Pad6 approximation

The univariate error formulas for Pad6 approximants and rational interpolants, which are repeated in Section 2, are generalized to the multivariate case in Section 4. We deal with "general order" multivariate Pad~ approximants and rational interpolants, where the numerator and denominator polynomials as well as the equations expressing the approximation order, can be chosen by the user of these...

On Error Formulas for Multivariate Polynomial Interpolation

In this paper we prove that the existence of an error formula of a form suggested in [2] leads to some very specific restrictions on an ideal basis that can be used in such formulas. As an application, we provide a negative answer to one version of the question posed by Carl de Boor (cf. [2]) regarding the existence of certain minimal error formulas for multivariate interpolation. §

On Error Formulas for Multivariate Interpolation

In this paper we prove that the existence of an error formula of a form suggested in [2] leads to some very specific restrictions on an ideal basis that can be used in such formulas. As an application, we provide a negative answer to one version of the question posed by Carl de Boor (cf. [2]) regarding the existence of certain minimal error formulas for multivariate interpolation.

Hermite-Pade' approximation and simultaneous quadrature formulas

We study the construction of a quadrature rule which allows the simultaneous integration of a given function with respect to different weights. This construction is built on the basis of simultaneous Padé approximation of a Nikishin system of functions. The properties of these approximants are used in the proof of convergence of the quadratures and positivity of the corresponding quadrature coe...

On Multivariate Birkhoff Rational Interpolation