Article ID Journal Published Year Pages File Type
4603109 Linear Algebra and its Applications 2008 15 Pages PDF
Abstract

In this paper, we present two fast numerical methods for computing the QR factorization of an n×n Cauchy-like matrix C, C=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. Exploiting the structure of this problem enables us to develop quadratic time, i.e., O(n2), QR factorization algorithms.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory