A reliable modification of the cross rule for rational Hermite interpolation (Q688096)

The values of a rational interpolation table can be obtained by using \textit{G. Classens'} cross rule [Numer. Math. 29, 227-231 (1978; Zbl 0375.65004)]. This rule fails if certain related values of the table are equal to each other; such neighbouring entries are combined in the so- called singular blocks. The aim of this paper is the introduction of a simple recursive algorithm for computing the values of neighbours of the singular block. This allows to compute entries in the table of rational interpolants even in the presence of singular blocks. An interesting numerical example is given.