The finite temperature effective potential of the Abelian Higgs Model is studied using the self-consistent composite operator method, which can be used to sum up the contributions of daisy and superdaisy diagrams. The effect of the momentum dependence of the effective masses is estimated by using a Rayleigh-Ritz variational approximation.

Microvibrations at frequencies between 1 and 1000 Hz generated by on-board equipment can propagate through a satellite's structure and hence signiicantly reduce the performance of sensitive payloads. This paper describes a Lagrange-Rayleigh-Ritz method for developing models suitable for the design of active control schemes. Here Loop Transfer Recovery based controller design methods are employe...

We present some new error estimates for the eigenvalues and eigenfunctions obtained by the Rayleigh-Ritz method, the common variational method to solve eigenproblems. The errors are bounded in terms of the error of the best approximation of the eigenfunction under consideration by functions in the ansatz space. In contrast to the classical theory, the approximation error of eigenfunctions other...

In the present paper, the free vibration of moderately thick trapezoidal plates has been studied. The analysis is based on the Mindlin shear deformation theory. The solutions are determined using the pb-2 Rayleigh-Ritz method. The transverse displacement and the rotations of the plate are approximated by Ritz functions defined as two dimensional polynomials of the trapezoidal domain variables a...

We derive error bounds for the Rayleigh-Ritz method for the approximation to extremal eigenpairs of a symmetric matrix. The bounds are expressed in terms of the eigenvalues of the matrix and the angle between the subspace and the eigenvector. We also present a sharp bound.

We derive error bounds for the Rayleigh-Ritz method for the approximation to extremal eigenpairs of a symmetric matrix. The bounds are expressed in terms of the eigenvalues of the matrix and the angle between the subspace and the eigenvector. We also present a sharp bound.

Finite dynamic element methods are interpreted as Rayleigh-Ritz methods where the trial functions depend linearly on the eigenparameter. The positive eigenvalues of the corresponding cubic matrix eigenvalue problem are proved to be upper bounds of eigenvalues of the original problem which are usually better than the bounds that one gets from the corresponding nite element method.

The Rayleigh–Ritz (rr) method is well known as a means of minimizing energy functionals. Despite this, the technique most often employed in practice for minimizing a functional is the numerical solution of the Euler–Lagrange (el) equations derived from the energy functional by variational minimization. In this article we employ the rr method specifically to determine the equilibrium shape of a ...

In this work we have proposed an improvement in the shape of the V-shaped microcantilever by varying the width profile. In this paper we have studied the variation of resonant frequency as a function of changes in profile determined by the length of the microcantilever, keeping constant the active area for binding. It is observed that for the optimized nonlinear profile the angle at the tip is ...

New bounds on the canonical angles between an invariant subspace of A and an approximating subspace by the differences between Ritz values and the targeted eigenvalues are obtained. From this result, various bounds are readily available to estimate how accurate the Ritz vectors computed from the approximating subspace may be, based on information on approximation accuracies in the Ritz values. ...