Loading...
On the Error in the Product QR Decomposition
Van Vleck, Erik S.
Van Vleck, Erik S.
Citations
Altmetric:
Abstract
We develop both a normwise and a componentwise error analysis for the QR factorization of long products of invertible matrices. We obtain global error bounds for both the orthogonal and upper triangular factors that depend on uniform bounds on the size of the local error, the local degree of nonnormality, and integral separation, a natural condition related to gaps between eigenvalues but for products of matrices. We illustrate our analytical results with numerical results that show the dependence on the degree of nonnormality and the strength of integral separation.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/090761562.
Date
2010-03-17
Journal Title
Journal ISSN
Volume Title
Publisher
Society for Industrial and Applied Mathematics
Collections
Research Projects
Organizational Units
Journal Issue
Keywords
QR decomposition, matrix product, integral separation
Citation
Van Vleck, Erik. "On the Error in the Product QR Decomposition." (2010) SIAM. J. Matrix Anal. & Appl., 31(4), 1775–1791. (17 pages). http://dx.doi.org/10.1137/090761562.