We present an acceleration of the well-established Krylov-Ritz methods to compute the sign function of large complex matrices, as needed in lattice QCD simulations involving the overlap Dirac operator at both zero and nonzero baryon density. Krylov-Ritz methods approximate the sign function using a projection on a Krylov subspace. To achieve a high accuracy this subspace must be taken quite lar...

I have been asked to discuss for you some applications of the Rayleigh-Ritz method in physics. Rather than at tempt to survey the whole of a discouragingly large field I have preferred to restrict my attention to some few topics from the theory of atomic and molecular structure. The application of the Rayleigh-Ritz method in this field has been carried out with some care and persistence, and th...

By the semi-inverse method proposed by He, a Lagrangian is established for the large deflection problem of thin circular plate. Ritz method is used to obtain an approximate analytical solution of the problem. First order approximate solution is obtained, which is similar to those in open literature. By Mathematica a more accurate solution can be deduced. 2002 Elsevier Science Inc. All rights re...

We make use of the Pad e approximants and Krylov's sequence x; Ax; ; : : :; A m?1 x in the projection methods to compute a few Ritz values of a hermitian matrix A of order n. This process consists of approaching the poles of R x () = ((I ?A) ?1 x; x), the mean value of the resolvant of A, by those of m ? 1=m] Rx (), where m ? 1=m] Rx () is the Pad e approximant of order m of the function R x ()...

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.

In this paper, a continuum model based on the nonlocal elasticity theory is developed for vibration analysis of embedded orthotropic circular and elliptical micro/nano-plates. The nano-plate is bounded by a Pasternak foundation. Governing vibration equation of the nonlocal nano-plate is derived using Nonlocal Classical Plate Theory (NCPT). The weighted residual statement and the Galerkin method...

Elastic stability of ring and stringer-stiffened cylindrical shells under axial, internal and external pressures is studied using Ritz method. The stiffeners are rings, stringers and their different arrangements at the inner and outer surfaces of the shell. Critical buckling loads are obtained using Ritz method. It has been found that the cylindrical shells with outside rings are more stable th...

A nonlinear Rayleigh-Ritz iterative (NRRIT) method for solving nonlinear eigenvalue problems is studied in this paper. It is an extension of the nonlinear Arnoldi algorithm due to Heinrich Voss. The effienicy of the NRRIT method is demonstrated by comparing with inverse iteration methods to solve a highly nonlinear eigenvalue problem arising from finite element electromagnetic simulation in acc...

The management problem of water reservoirs can be formulated as a stochastic optimal control (SOC) problem, where the objective function is an aggregated cost that accounts for the interests acting in the water system (e.g. hydropower production, irrigation supply, etc.) and the design variable is the reservoirs release policy. Solving the SOC problem through stochastic dynamic programming is o...

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...