Unattainable points in multivariate rational interpolation
The concept of unattainability arises in rational interpolation when one wants to find the interpolatory solution of \(t-p/q\) \((p,q\) polynomials) by solving the lineralized interpolation problem \(qf-p\) first; the univariate situation has been studied extensively by \textit{G. Claessens} [J. Approximation Theory 22, 150-160 (1978; Zbl 0386.41002)]. The authors extend one of the univariate results to the multivariate case (concerning the possible common factors of the minimal solution \(p\), \(q\) of the linearized problem) and show through very nice examples that other results can not be extended (concerning the `triangular' and `block- diagonal' structure of the pointsets in \(I-0.06\text{cm }N^ 2\) for which the irreducible form of the minimal rational interpolant is the same).
scientific article; zbMATH DE number 222123