RAYLEIGH-RITZ AND LANCZOS METHODS FOR SYMMETRICAL MATRIX PENCILS

We are concerned with eigenvalue problems for definite and indefinite symmetric matrix pencils. First, Rayleigh-Ritz methods are formulated and, using Krylov subspaces, a convergence analysis is presented for d efinite pencils. Second, generalized symmetric Lanczos algorithms are introduced as a special Rayleigh-Ritz method. In particular, an a post eriori convergence criterion is demonstrated by using residuals. Local convergence to real and nonreal eigenvalues is also discussed. Numeri cal examples concerning vibrations of damped cantilever beams are incl uded.