This paper demonstrates the possibility of incorporating load-dependent Ritz vectors, as an alternative to modal parameters, into a Bayesian probabilistic framework for detecting damages in a structure. Recent research has shown that it is possible to extract load-dependent Ritz vectors from vibration tests [2]. This paper shows that load-dependent Ritz vectors have the following potential adva...

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...

A procedure is presented for the computation of bounds to eigenvalues of the generalized hermitian eigenvalue problem and to the standard hermitian eigenvalue problem. This procedure is applicable to iterative subspace eigenvalue methods and to both outer and inner eigenvalues. The Ritz values and their corresponding residual norms, all of which are computable quantities, are needed by the proc...

This paper demonstrates the possibility of incorporating load-dependent Ritz vectors as an alternative to modal parameters into a Bayesian probabilistic framework for detecting damages in a structure. Recent research has shown that it is possible to extract load-dependent Ritz vectors from vibration tests. This paper shows that load-dependent Ritz vectors have the following potential advantages...

The A-gradient minimization of the Rayleigh quotient allows to construct robust and fastconvergent eigensolvers for the generalized eigenvalue problem for (A,M) with symmetric and positive definite matrices. The A-gradient steepest descent iteration is the simplest case of more general restarted Krylov subspace iterations for the special case that all step-wise generated Krylov subspaces are tw...

The usual estimates for conjugate gradients (CG) specify a non–trivial rate of convergence right from the beginning. We investigate situations where the same can be said for Ritz values (considered as approximations to eigenvalues). We investigate the effect on the convergence behaviour of Ritz values of multiplying the weight functions by certain functions of polynomial growth. This will be sh...

Modal parameters obtained from modal testing (such as modal vectors, natural frequencies, and damping ratios) have been used extensively in system identi"cation, "nite element model updating, and structural health monitoring. As an alternative to modal vectors, load-dependent Ritz vectors have been shown useful in various areas of structural dynamics such as model reduction and damage detection...

We show that arbitrary convergence behavior of Ritz values is possible in the Arnoldi method and we give two parametrizations of the class of matrices with initial Arnoldi vectors that generates prescribed Ritz values (in all iterations). The second parametrization enables us to prove that any GMRES residual norm history is possible with any prescribed Ritz values (in all iterations), provided ...