A framework for robust eigenvalue and eigenvector error estimation and Ritz value convergence enhancement

نویسنده

  • JEFFREY S. OVALL
چکیده

We present a general framework for the a posteriori estimation and enhancement of error ineigenvalue/eigenvector computations for symmetric and elliptic eigenvalue problems, and provide detailedanalysis of a specific and important example within this framework—finite element methods with continuous,affine elements. A distinguishing feature of the proposed approach is that it provides provably efficient andreliable error estimation under very realistic assumptions, not only for single, simple eigenvalues, but also forclusters which may contain degenerate eigenvalues. We reduce the study of the eigenvalue/eigenvector errorestimators to the study of associated boundary value problems, and make use of the wealth of knowledgeavailable for such problems. Our choice of a posteriori error estimator, computed using hierarchical bases,very naturally offers a means not only for estimating error in eigenvalue/eigenvector computations, but alsocheaply accelerating the convergence of these computations—sometimes with convergence rates which arenearly twice that of the unaccelerated approximations.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the Convergence of Q-ritz Pairs and Refined Q-ritz Vectors for Quadratic Eigenvalue Problems

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...

متن کامل

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...

متن کامل

Bayes, E-Bayes and Robust Bayes Premium Estimation and Prediction under the Squared Log Error Loss Function

In risk analysis based on Bayesian framework, premium calculation requires specification of a prior distribution for the risk parameter in the heterogeneous portfolio. When the prior knowledge is vague, the E-Bayesian and robust Bayesian analysis can be used to handle the uncertainty in specifying the prior distribution by considering a class of priors instead of a single prior. In th...

متن کامل

A Study of MCA Learning Algorithm for Incident Signals Estimation

Many signal subspace-based approaches have already been proposed for determining the fixed Direction of Arrival (DOA) of plane waves impinging on an array of sensors. Two procedures for DOA estimation based neural network are presented. Firstly, Principal Component Analysis (PCA) is employed to extract the maximum eigenvalue and eigenvector from signal subspace to estimate DOA. Secondly, Minor ...

متن کامل

Robust residual a posteriori error estimators for the Reissner-Mindlin eigenvalues system

We consider a conforming finite element approximation of the Reissner-Mindlin eigenvalue system, for which a robust a posteriori error estimator for the eigenvector and the eigenvalue errors is proposed. For that purpose, we first perform a robust a priori error analysis without strong regularity assumption. Upper and lower bounds are then obtained up to higher order terms that are superconverg...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010