Fast QR factorization of Cauchy-like matrices (Q2465328)

The paper presents two fast numerical methods for computing the QR factorization of an \(n\times n\) Cauchy-like matrix \(C\), \(C=\text{QR}\), with data points lying on the real axis or on the unit circle in the complex plane. It is shown that the rows of the \(Q\)-factor of \(C\) are the eigenvectors of a rank structured matrix partially determined by some prescribed spectral data. This property establishes a basic connection between the computation of \(Q\) and the solution of an inverse eigenvalue problem for a rank structured matrix.