Bidiagonal decomposition of rectangular totally positive Said–Ball–Vandermonde matrices: Error analysis, perturbation theory and applications

Abstract

An algorithm for computing the bidiagonal decomposition of Said–Ball–Vandermonde matrices in the rectangular case is presented, which allows one to use known algorithms for totally positive matrices represented by their bidiagonal decomposition. The algorithm is fast and possesses high relative accuracy. The error analysis of the algorithm is also addressed, along with the perturbation theory for the bidiagonal factorization of totally positive Said–Ball–Vandermonde matrices. Some numerical experiments showing the good behavior of the algorithm are included.