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...
متن کاملRelative perturbation of invariant subspaces ∗
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.
متن کاملPerturbation analysis of Lagrangian invariant subspaces of symplectic matrices
Lagrangian invariant subspaces for symplectic matrices play an important role in the numerical solution of discrete time, robust and optimal control problems. The sensitivity (perturbation) analysis of these subspaces, however, is a difficult problem, in particular, when the eigenvalues are on or close to some critical regions in the complex plane, such as the unit circle. We present a detailed...
متن کاملPerturbation, Computation and Refinement of Invariant Subspaces for Matrix Polynomials
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...
متن کاملOn a Perturbation Bound for Invariant Subspaces of Matrices
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: Journal of Mathematical Analysis and Applications
سال: 1996
ISSN: 0022-247X
DOI: 10.1006/jmaa.1996.0011