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

## TL;DR

This paper derives computationally efficient bounds for residual norm ratios in refined and Rayleigh-Ritz projection methods, aiding in their comparison and selection.

## Contribution

It introduces a new, less costly bound for residual norms, enhancing practical assessment of the two projection methods.

## Key findings

- Derived a new residual norm ratio bound
- Bound is computationally less expensive
- Facilitates practical comparison of 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.