Perturbation Analyses for the QR Factorization
SIAM Journal on Matrix Analysis and Applications
Lyapunov Spectral Intervals: Theory and Computation
SIAM Journal on Numerical Analysis
A periodic Krylov-Schur algorithm for large matrix products
Numerische Mathematik
On the Error in QR Integration
SIAM Journal on Numerical Analysis
On the error in approximating stability spectra for discrete dynamical systems
Mathematics and Computers in Simulation
Advances in Computational Mathematics
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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.