## A block Rayleigh quotient iteration with local quadratic convergence

Jean-Luc Fattebert

### Abstract

We present an iterative method, based on a block generalization of the Rayleigh Quotient Iteration method, to search for the $p$ lowest eigenpairs of the generalized matrix eigenvalue problem $Au=\lambda Bu$. We prove its local quadratic convergence when $B^{-1}A$ is symmetric. The benefits of this method are the well-conditioned linear systems produced and the ability to treat multiple or nearly degenerate eigenvalues.

Full Text (PDF) [179 KB]

### Key words

Subspace iteration, Rayleigh Quotient Iteration, Rayleigh-Ritz procedure.

65F15.