Inversion formulas and fast algorithms for Löwner-Vandermonde matrices

AbstractMatrices consisting of two parts one of Vandermonde and the other of Löwner type are considered. Inversion formulas (also for one-sided inverses) are presented. Moreover, in the nonsingular case the parameters of the inversion formulas are described in terms of the evaluation of numerator and denominator polynomials which constitute the solution of associated rational interpolation problems. These results can be used to establish an algorithm for the solution of Löwner-Vandermonde systems of equations with O(n log2 n) complexity