The convergence of Rayleigh-Ritz approximations

Accuracy of Rayleigh- Ritz Approximations

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. ...

Dependence of the rate of convergence of the Rayleigh-Ritz method on a nonlinear parameter.

Numerical computation of optimum values for nonlinear parameters in a Rayleigh-Ritz variational trial function is considerably more difBcult than numerical computation of optimum values for linear parameters. Thus, an analytic understanding of the mechanisms that determine these optimum values can be quite useful. Uniform asymptotic expansions can be used to explore these mechanisms for the non...

Orders of convergence of the rayleigh-ritz and weinstein-bazley methods.

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...

Generalizations of Harmonic and Refined Rayleigh–ritz

Abstract. We investigate several generalizations of the harmonic and refined Rayleigh–Ritz method. These may be practical when one is interested in eigenvalues close to one of two targets (for instance, when the eigenproblem has Hamiltonian structure such that eigenvalues come in pairs or quadruples), or in rightmost eigenvalues close to (for instance) the imaginary axis. Our goal is to develop...