On refined Ritz vectors and polynomial characterization
نویسندگان
چکیده
منابع مشابه
The convergence of harmonic Ritz values, harmonic Ritz vectors and refined harmonic Ritz vectors
This paper concerns a harmonic projection method for computing an approximation to an eigenpair (λ, x) of a large matrix A. Given a target point τ and a subspace W that contains an approximation to x, the harmonic projection method returns an approximation (μ + τ, x̃) to (λ, x). Three convergence results are established as the deviation of x from W approaches zero. First, the harmonic Ritz value...
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For a given subspace, the q-Rayleigh-Ritz method projects the large quadratic eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar to the Rayleigh-Ritz method for the linear eigenvalue problem, the q-Rayleigh-Ritz method defines the q-Ritz values and the q-Ritz vectors of the QEP with respect to the projection subspace. We analyze the convergence of the method when the...
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After reviewing the harmonic Rayleigh–Ritz approach for the standard and generalized eigenvalue problem, we discuss different extraction processes for subspace methods for the polynomial eigenvalue problem. We generalize the harmonic and refined Rayleigh–Ritz approach, which are new approaches to extract promising approximate eigenpairs from a search space. We give theoretical as well as numeri...
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Abstract. We investigate several generalizations of the harmonic and refined Rayleigh–Ritz method. These may be practical when one is interested in eigenvalues close to one of two targets (for instance, when the eigenproblem has Hamiltonian structure such that eigenvalues come in pairs or quadruples), or in rightmost eigenvalues close to (for instance) the imaginary axis. Our goal is to develop...
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The following estimate for the Rayleigh–Ritz method is proved: |λ̃−λ||(ũ,u)| ≤ ‖Aũ− λ̃ũ‖sin∠{u;Ũ}, ‖u‖= 1. Here A is a bounded self-adjoint operator in a real Hilbert/euclidian space, {λ,u} one of its eigenpairs, Ũ a trial subspace for the Rayleigh–Ritz method, and {λ̃, ũ} a Ritz pair. This inequality makes it possible to analyze the fine structure of the error of the Rayleigh–Ritz method, in part...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2014
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2014.01.005