Global Identities in the Non-normal Newton-Padé Approximation Table Original Research Article

This note is concerned with the Newton-Padé table containing rational interpolants with varying numerator and denominator degrees. In the general case some entries of the table can be equal, combined in so-called singular blocks. Any singular block in this non-normal Newton-Padé approximation table consists of squares forming a symmetric tail. It is the aim of this note to present global identities between neighboring entries of a singular block. In particular, we generalize Cordellier′s identities for Padé approximation. The resulting algorithmic aspects, e.g., a reliable modification of Claessens′ cross-rule (G. Claessens, Numer. Math.29 (1978), 227-231 ), are discussed in (B. Beckermann and C. Carstensen, Numer. Algorithms3 (1992), 29-44).