Bounds for Eigenvalues of Some Differential Operators by the Rayleigh-Ritz Method

Optimal a priori error bounds for the Rayleigh-Ritz method

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.

Damage Detection of Bridge by Rayleigh-Ritz Method

As a result of environmental and accidental actions, damage occurs in structures. The early detection of any defect can be achieved by regular inspection and condition assessment. In this way, the safety and reliability of structures can be increased. This paper is devoted to propose a new and effective method for detecting, locating, and quantifying beam-like structures. This method is based o...

Optimal a priori error bounds for the Rayleigh - Ritz method by Gerard

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.

Commutator Bounds for Eigenvalues of Some Diierential Operators

Fluid drop shape determination by the Rayleigh--Ritz minimization 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 ...