Global identities in the non-normal Newton--Padé approximation table
The block structure in a Newton-Padé table is studied. If a vector \((z_ 0,z_ 1,\dots)\) of interpolation knots in the complex plane \(\mathbb{C}\) and a sufficiently smooth function \(f\) is given, then the Newton- Padé table is the doubly infinity array of rational functions \(r_{mn}\) of degree at most \(m\) and \(n\) that interpolate \(f\) in the points \(z_ 0,z_ 1,\dots, z_{m+n}\). (In the case that a proper interpolant does not exist, the linearized version is used.) In the paper the structure of singular blocks is investigated, identities between adjacent entries of singular blocks are presented, and in particular Cordellier's identities are generalized to the Newton-Padé table. Such identities lead to algorithms for calculating entries in a Newton-Padé table. Such identities lead to algorithms for calculating entries in a Newton-Padé table in an efficient way.
scientific article; zbMATH DE number 370440