QR factorization of confluent Vandermonde matrices

Abstract

An algorithm for computing the QR factors of a complex column confluent Vandermode matrix V of dimension m*n is introduced. The complexity of the algorithm is O(mn). Such an algorithm allows for a saving of an order of magnitude when solving systems involving such a matrix in the least squares sense. Such matrices occur when estimating the amplitude of complex exponentials (as in linear systems impulse response), and some modes are repeated.< >