Generalized-confluent Cauchy and Cauchy-Vandermonde matrices

The so-called Generalized-Confluent Cauchy-Vandermonde (GCCV) matrices of t he form [C,V] consisting of a generalized-confluent Cauchy part C and a gen eralized-confluent Vandermonde part V are considered. A simple relationship between GCCV and classical confluent Cauchy-Vandermonde (CCV) matrices is given. This leads to the reduction of the displacement structure, inversion formulas and factorizations of GCCV matrices, and the interpolation interp retations of linear systems with such GCCV coefficient matrices as tangenti al interpolation problems to the corresponding results of CCV matrices. The criteria of invertibility and (left, right) inversion formulas for such ma trices are given. All results are stated for the general case of multiple i nterpolation nodes, extending the work of Heinig, and Vavrin among others. (C) 2000 Elsevier Science Inc. All rights reserved.