We are not able to resolve this OAI Identifier to the repository landing page. If you are the repository manager for this record, please head to the Dashboard and adjust the settings.
The leverage scores of a full-column rank matrix A are the squared row norms of any orthonormal basis for range (A). We show that corresponding leverage scores of two matrices A and A + ΔA are close in the relative sense if they have large magnitude and if all principal angles between the column spaces of A and A + ΔA are small. We also show three classes of bounds that are based on perturbation results of QR decompositions. They demonstrate that relative differences between individual leverage scores strongly depend on the particular type of perturbation ΔA. The bounds imply that the relative accuracy of an individual leverage score depends on its magnitude and the two-norm condition of A if ΔA is a general perturbation; the two-norm condition number of A if ΔA is a perturbation with the same normwise row-scaling as A; (to first order) neither condition number nor leverage score magnitude if ΔA is a componentwise row-scaled perturbation. Numerical experiments confirm the qualitative and quantitative accuracy of our bounds.National Science Foundation (U.S.) (Grant CCF-1145383
Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.