On Residual norms in the Rayleigh-Ritz and refined Projection methods
arXiv:1902.08057h-index: 2
Originality Synthesis-oriented
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Provides a practical tool for numerical linear algebra practitioners to choose between two projection methods without full computation.
The paper derives computationally cheaper bounds for comparing residual norms in refined and Rayleigh-Ritz projection methods, enabling practical assessment of which method is superior.
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.