Spectral Rayleigh–Schrödinger Series Revisited

Abstract

Rayleigh–Schrödinger series for perturbation bounds of spectral elements is revisited. The convergence radius is estimated for bases of spectral subspaces. Applications to both Hessenberg and Hermitian matrices are developed, which are useful in spectral approximation with numerical methods.

Keywords:

• Eigenvalues
• Eigenvectors
• QR algorithm
• Rayleigh–Schrödinger series
• Spectral subspaces

AMS Subject Classification:

• 15A18
• 15A21
• 15A42
• 65F15
• 65F35

ACKNOWLEDGMENT

This research was partially supported by the Belgian Fonds de la Recherche Scientifique (FNRS) during 2007 at the Facultés universitaires catholiques de Mons (FUCaM).