Perturbation expansions for invariant subspaces
نویسندگان
چکیده
منابع مشابه
Perturbation of invariant subspaces ∗
We consider two different theoretical approaches for the problem of the perturbation of invariant subspaces. The first approach belongs to the standard theory. In that approach the bounds for the norm of the perturbation of the projector are proportional to the norm of perturbation matrix, and inversely proportional to the distance between the corresponding eigenvalues and the rest of the spect...
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In this paper we consider the upper bound for the sine of the greatest canonical angle between the original invariant subspace and its perturbation. We present our recent results which generalize some of the results from the relative perturbation theory of indefinite Hermitian matrices.
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Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of invariant subspac...
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Given a nonsymmetric matrix A, we investigate the effect of perturbations on an invariant subspace of A. The result derived in this paper is less restrictive on the norm of the perturbation and provides a potentially tighter bound compared to Stewart’s classical result. Moreover, we provide norm estimates for the remainder terms in well-known perturbation expansions for invariant subspaces, eig...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1991
ISSN: 0024-3795
DOI: 10.1016/0024-3795(91)90212-f