On a Subspace Perturbation Problem
نویسنده
چکیده
We discuss the problem of perturbation of spectral subspaces for linear self-adjoint operators on a separable Hilbert space. Let A and V be bounded self-adjoint operators. Assume that the spectrum of A consists of two disjoint parts σ and Σ such that d = dist(σ,Σ) > 0. We show that the norm of the difference of the spectral projections EA(σ) and EA+V ( {λ | dist(λ, σ) < d/2} ) for A and A+ V is less then one whenever either (i) ‖V ‖ < 2 2+π d or (ii) ‖V ‖ < 1 2 d and certain assumptions on the mutual disposition of the sets σ and Σ are satisfied.
منابع مشابه
Some Sharp Norm Estimates in the Subspace Perturbation Problem
We discuss the spectral subspace perturbation problem for a selfadjoint operator. Assuming that the convex hull of a part of its spectrum does not intersect the remainder of the spectrum, we establish an a priori sharp bound on variation of the corresponding spectral subspace under off-diagonal perturbations. This bound represents a new, a priori, tanΘ Theorem. We also extend the Davis–Kahan ta...
متن کاملEigenvalue Perturbation and Generalized Krylov Subspace Method
In this paper, we study the computational aspect of eigenvalue perturbation theory. In previous research, high order perturbation terms were often derived from Taylor series expansion. Computations based on such an approach can be both unstable and highly complicated. We present here with an approach based on the diierential formulation of perturbation theory where the high order perturbation c...
متن کاملSensitivity eigenanalysis for single shift-invariant subspace-based methods
A signal eigenvalue sensitivity analysis for subspace-based methods that exploit the shift-invariance property present in the signal subspace is considered. It is proved that signal eigenvalues are rather insensitive to small perturbations in the data provided the dimension of the problem is large enough and the eigenvalues themselves are not extremely close to each other. In addition, bounds o...
متن کاملA New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems
In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.
متن کاملSubspace Receiver Techniques for DS-CDMA Systems in Space Diffused Vector Channels
This work is motivated by the fact that basestation receiver performance degrades significantly in spatially diffused multipath channels. Herein, this problem is addressed for array DS-CDMA systems in spatially diffused vector channels. Firstly, multipath spatial diffusion is cast as a signal model perturbation problem and then two subspace based receiver techniques are proposed that effectivel...
متن کاملOn the Properties for Iteration of a Compact Operator with Unstructured Perturbation
We consider certain speed estimates for Krylov subspace methods (such as GMRES) when applied upon systems consisting of a compact operator K with small unstructured perturbation B. Information about the decay of singular values of K is also assumed. Our main result is that the Krylov method will perform initially at superlinear speed when applied upon such pre-conditioned system. However, with ...
متن کامل