Generalized confluent Cauchy–Vandermonde matrices: displacement structures, inversion formulas and tangential interpolations

Generalized confluent Cauchy and Cauchy–Vandermonde matrices are introduced. These two kinds of matrices generalize the ordinary Cauchy and Cauchy–Vandermonde matrices with multiple nodes studied earlier by various authors. By using displacement structure theory fast inversion formulas for these matrices are derived. The tangential interpolation interpretations for associated linear systems with such matrices are given. The fast algorithm for solving this kind of linear systems are also considered.