Generalized Cauchy-Vandermonde matrices
This paper thoroughly deals with matrices of the form \([C V]\) consisting of a generalized Cauchy matrix \(C\) and a generalized Vandermonde matrix \(V.\) The displacement structure of these generalized Cauchy-Vandermonde (CV) matrices is used in order to obtain formulas for the inverse of such a matrix involving solutions of the so-called fundamental equations. Linear systems of equations with a CV coefficient matrix may be interpreted as tangential interpolation problems. This leads to the concept of left and right fundamental matrices for (arbitrary) nonsingular CV matrices. A careful discussion of recursions for the fundamental matrices gives rise to fast algorithms (of Levinson and Schur types) for evaluating the inverse of a CV matrix.
scientific article; zbMATH DE number 1109494