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...

FOM and GMRES are Krylov subspace iterative methods for solving nonsymmetric linear systems. The Ritz values are approximate eigenvalues, which can be computed cheaply within these algorithms. In this paper, we generalise the concept of Harmonic Ritz values, introduced by Paige et al. for symmetric matrices, to nonsymmetric matrices. We show that the zeroes of the residual polynomials of FOM an...

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...

In engineering applications, especially in the field of modern military defence, the cylindrical shells, conical shells and coupled conical-cylindrical shells are basically simplified models of many types of weapons and equipment, such as aircraft, missiles, and submarines. The study of free vibrational characteristics of cylindrical shells is comprehensive. Initially, researchers1-5 investigat...

The IDR method of Sonneveld and van Gijzen [SIAM J. Sci. Comput., 31:1035–1062, 2008] is shown to be a Petrov-Galerkin (projection) method with a particular choice of left Krylov subspaces; these left subspaces are rational Krylov spaces. Consequently, other methods, such as BiCGStab and ML(s)BiCGStab, which are mathematically equivalent to some versions of IDR, can also be interpreted as Petro...

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...

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. ...

A fluctuation law of the energy in freely-decaying, homogeneous and isotropic turbulence is derived within a Gaussian closure ansatz for 3D incompressible flow. In particular, a fluctuation-dissipation relation is derived which relates the strength of a stochastic backscatter term in the energy decay equation to the mean of the energy dissipation rate. The theory is based on the so-called “effe...