Confluent polynomial Vandermonde-like matrices: displacement structures, inversion formulas and fast algorithm

Abstract

In the present paper we use the displacement structure approach to introduce a new class of what are called confluent polynomial Vandermonde-like matrices, which generalize the ordinary simple nodes polynomial Vandermonde matrices studied earlier by different authors. The displacement structure approach leads to the explicit inversion formulas for confluent polynomial Vandermonde-like matrices and fast algorithms for inversion and for solving the associated linear systems.