Bounds on the error of an approximate invariant subspacefor non-self-adjoint matrices |
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Authors: | Moshe Haviv Ya'acov Ritov |
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Affiliation: | (1) Department of Statistics, The Hebrew University of Jerusalem, 91905 Jerusalem, Israel , IL;(2) Department of Econometrics, The University of Sydney, Sydney, NSW 2006, Australia , AU |
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Abstract: | Summary. Suppose one approximates an invariant subspace of an matrix in which in not necessarily self--adjoint. Suppose that one also has an approximation for the corresponding eigenvalues. We consider the question of how good the approximations are. Specifically, we develop bounds on the angle between the approximating subspace and the invariant subspace itself. These bounds are functions of the following three terms: (1) the residual of the approximations; (2) singular--value separation in an associated matrix; and (3) the goodness of the approximations to the eigenvalues. Received December 1, 1992 / Revised version received October 20, 1993 |
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Keywords: | Mathematics Subject Classification (1991): 65F15 |
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