The goal of this paper is to increase our understanding of harmonic Rayleigh– Ritz for real symmetric matrices. We do this by discussing different, though related topics: a priori error analysis, a posteriori error analysis, a comparison with refined Rayleigh–Ritz and the selection of a suitable harmonic Ritz vector.

It is essential to understand the consumption pattern of food and how it changes over time to formulate sound economic policies as well as marketing and pricing strategies. In this study, we estimate the Quadratic Almost Ideal Demand System with six rounds of the Family Income Expenditure Survey exploiting the conditional linearity of the demand system. We find that the Filipino diet has become...

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...

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...

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...

The block preconditioned steepest descent iteration is an iterative eigensolver for subspace eigenvalue and eigenvector computations. An important area of application of the method is the approximate solution of mesh eigenproblems for self-adjoint and elliptic partial differential operators. The subspace iteration allows to compute some of the smallest eigenvalues together with the associated i...