On Residual norms in the Rayleigh-Ritz and refined Projection methods

Abstract

This paper derives bounds for the ratio of residual norms in the refined and Rayleigh- Ritz projection methods. To do this, it uses the Least squares and line search projection method proposed in [6]. The bound derived in this paper is less costly to compute. Further, it is practically useful to assess the superiority of the refined and the Rayleigh-Ritz projection methods one over the other.