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On perturbation bounds for the QR factorization. (English) Zbl 0816.15010

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.

MSC:

15A23 Factorization of matrices
15A45 Miscellaneous inequalities involving matrices
65F05 Direct numerical methods for linear systems and matrix inversion
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