A unified approach to Loewner and Hankel matrices
The elements of Loewner matrices have the form \[ (c_ i-d_ j)/(y_ i-z_ j) \] and are associated with the theory of interpolation at simple points by rational functions. In order to deal with interpolation of both function and derivatives a more general type of matrix has to be defined; this includes the standard Loewner matrix at one extreme and Hankel matrices at the other (when all the data is at one point). The paper contains the study of these matrices and the associated interpolation problem, and includes characterization of nonsolvable cases by means of rank properties of the Loewner matrix. In order to simplify the presentation of the rather complicated material the paper is in three parts. One for the presentation of definitions and theorems, the next for appropriate proofs and the final one contains examples to illustrate the theory.
scientific article; zbMATH DE number 4171129