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On the Eigensystems of Graded Matrices

dc.contributor.authorStewart, G. W.en_US
dc.description.abstractInformally a graded matrix is one whose elements show a systematic decrease or increase as one passes across the matrix. It is well known that graded matrices often have small eigenvalues that are determined to high relative accuracy. Similarly, the eigenvectors can have small components that are nonetheless well determined. In this paper, we give approximations to the eigenvalues and eigenvectors of a graded matrix in terms of a base matrix that show how these phenomena come about. This approach provides condition numbers for eigenvalues and individual components of the eigenvectors. The results are applied to derive related results for the singular value decomposition. (Also cross-referenced as UMAICS-TR-2000-01)en_US
dc.format.extent2040324 bytes
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-4099en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-2000-01en_US
dc.titleOn the Eigensystems of Graded Matricesen_US
dc.typeTechnical Reporten_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtUMIACS Technical Reportsen_US

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