One application of harmonic Ritz values is to approximate, with a projection method, the interior eigenvalues of a matrix A while avoiding the explicit use of the inverse A. In this context, harmonic Ritz values are commonly derived from a Petrov-Galerkin condition for the residual of a vector from the test space. In this paper, we investigate harmonic Ritz values from a slightly different pers...

Experimentally determined natural frequencies and modes shapes are presented for an elastically point-supported isotropic plate with attached masses under impulsive loading. These results are compared to frequencies and to modes shapes determined from the Rayleigh–Ritz method and a finite element analysis using COMSOL. Accelerometers mounted at three locations on the plate, provide input for ME...

In this addendum to an earlier paper by the author, it is shown how to compute a Krylov decomposition corresponding to an arbitrary Rayleigh-Quotient. This decomposition can be used to restart an Arnoldi process, with a selection of the Ritz vectors corresponding to the Rayleigh quotient. ABSTRACT In this addendum to an earlier paper by the author, it is shown how to compute a Krylov decomposit...

In this paper, we study the Rayleigh-Ritz approximation for the eigenproblem of periodic matrix pairs. We show the convergence of the Ritz value and periodic Ritz vectors. Furthermore, we prove the convergence of refined periodic Ritz vectors and propose an efficient algorithm for computing the refined periodic Ritz vectors. The numerical result shows that the refinement procedure produces an e...

this paper may be regarded as a new numerical method for the analysis of triangular thin plates using the natural area coordinates. previous studies on the solution of triangular plates with different boundary conditions are mostly based on the rayleigh-ritz principle which is performed in the cartesian coordinates. consequently, manipulation of the geometry and numerical calculation of the int...

where the values of the constants Ai, A2 and Pi, P2 are not simultaneously zero. Several methods have been proposed to determine the proper elements (i.e. eigenvalues and eigenfunctions) of Sturm-Liouville equations. Most of them have been reviewed by Kopal [1], but we shall examine one of them, the so called Rayleigh-Ritz method, in order to explain the main defect they have in common and to j...