A procedure is presented for the computation of bounds to eigenvalues of the generalized hermitian eigenvalue problem and to the standard hermitian eigenvalue problem. This procedure is applicable to iterative subspace eigenvalue methods and to both outer and inner eigenvalues. The Ritz values and their corresponding residual norms, all of which are computable quantities, are needed by the proc...

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...

This paper demonstrates the possibility of incorporating load-dependent Ritz vectors as an alternative to modal parameters into a Bayesian probabilistic framework for detecting damages in a structure. Recent research has shown that it is possible to extract load-dependent Ritz vectors from vibration tests. This paper shows that load-dependent Ritz vectors have the following potential advantages...

The A-gradient minimization of the Rayleigh quotient allows to construct robust and fastconvergent eigensolvers for the generalized eigenvalue problem for (A,M) with symmetric and positive definite matrices. The A-gradient steepest descent iteration is the simplest case of more general restarted Krylov subspace iterations for the special case that all step-wise generated Krylov subspaces are tw...

In this paper, a shallow Ritz-type neural network for solving elliptic equations with delta function singular sources on an interface is developed. There are three novel features in the present work; namely, (i) singularity naturally removed, (ii) level set introduced as feature input, (iii) it completely shallow, comprising only one hidden layer. We first introduce energy functional of problem...

The usual estimates for conjugate gradients (CG) specify a non–trivial rate of convergence right from the beginning. We investigate situations where the same can be said for Ritz values (considered as approximations to eigenvalues). We investigate the effect on the convergence behaviour of Ritz values of multiplying the weight functions by certain functions of polynomial growth. This will be sh...