Fast algorithms of Björck-Pereyra type for solving Cauchy-Vandermonde linear systems Original Research Article

Cauchy-Vandermonde matrices and their relationship with rational interpolation problems are studied. Fast algorithms for solving the corresponding linear systems are presented. They are explicit algorithms that generalize in a natural way Björck-Pereyra algorithms for solving Vandermonde linear systems. The total positivity of Cauchy-Vandermonde matrices is analyzed and some applications are provided.