Van Vleck, Erik S.2015-03-302015-03-302010-03-17Van 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.https://hdl.handle.net/1808/17246This is the published version, also available here: http://dx.doi.org/10.1137/090761562.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.QR decompositionmatrix productintegral separationArticle10.1137/090761562openAccess