The calculation of a few interior eigenvalues of a matrix has not received much attention in the past, most methods being some spin-off of either the complete eigenvalue calculation or a subspace method designed for the extremal part of the spectrum. The reason for this could be the rather chaotic behaviour of most methods tried. Only 'shift and invert' and polynomial iteration seemed to have a...

We present experiments with two new solvers for large sparse symmetric matrix eigenvalue problems: (1) the implicitly restarted Lanc-zos algorithm and (2) the Jacobi-Davidson algorithm. The eigenvalue problems originate from in the computation of a few of the lowest frequencies of standing electromagnetic waves in cavities that have been discretized by the nite element method. The experiments h...

The Lanczos process is a well known technique for computing a few, say k, eigenvalues and associated eigenvectors of a large symmetric n×n matrix. However, loss of orthogonality of the computed Krylov subspace basis can reduce the accuracy of the computed approximate eigenvalues. In the implicitly restarted Lanczos method studied in the present paper, this problem is addressed by fixing the num...

We explore singularly perturbed convection-diffusion equations in a circular domain. Considering boundary layer analysis of the singularly perturbed equations and we show convergence results. In view of numerical analysis, We discuss approximation schemes, error estimates and numerical computations. To resolve the oscillations of classical numerical solutions due to the stiffness of our problem...

In a recent paper Sima, Van Huffel and Golub [Regularized total least squares based on quadratic eigenvalue problem solvers. BIT Numerical Mathematics 44, 793 812 (2004)] suggested a computational approach for solving regularized total least squares problems via a sequence of quadratic eigenvalue problems. Taking advantage of a variational characterization of real eigenvalues of nonlinear eigen...