On perturbation bounds for the QR factorization (Q1347219)

Let \(A\) be a real \(m \times n\) matrix with \(\text{rank} A = n\). The QR factorization of \(A\) is a decomposition of the form \(A = QR\), where \(R\), the triangular factor, is an upper triangular \(n \times n\) matrix with positive diagonal elements and \(Q\), the orthogonal factor, is an \(m \times n\) matrix satisfying \(Q^ TQ = I\). In this paper the author derives certain new perturbation bounds for \(Q\) which improve the known bounds in the literature. The paper ends with a numerical example.