Recursive solution of Löwner-Vandermonde systems of equations. I

AbstractAn O(n2) algorithm for the solution of a linear system the n × n coefficient matrix of which consists of a Vandermonde and a Löwner part is presented. In the first part of the algorithm the corresponding Vandermonde system is solved. In the second part the last rows of the Vandermonde matrix are successively replaced by rows of the Löwner structure. The algorithm is convenient if the Vandermonde part is dominant. The main tool is the connection of such systems with rational interpolation problems