A new approach to vector-valued rational interpolation
The author gave the general framework within which a whole family of vector-valued rational interpolants was defined. The author introduced three different types of criteria to obtain the three types of rational interpolation procedures and developed algorithms for constructing the resulting rational functionals. The author derived determinantal representation for these rational interpolants. These determinantal representations may serve as a useful tool in the (de Montessus type) convergence analysis of the interpolants as the degree of their numerators tends to infinity while the degree of their denominators is kept fixed. This approach was used successfully in the paper of \textit{A. Sidi} [''Rational approximations from power series of vector-valued mermorphic function'', J. Approx. Theory 77, No.1, 89--111 (1994; Zbl 0808.41010)].
scientific article; zbMATH DE number 2137004