Fast algorithms of Bjo¨rck-Pereyra type for solving Cauchy-Vandermonde linear systems

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 Bjorck-Pereyra algorithms for solving Vandermonde linear systems. The total positivity of Cauchy-Vandermonde matrices is analyzed and some applications are provided.

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