A block Rayleigh Quotient Iteration with local quadratic convergence

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 Λu = λBu. We prove its local quadratic convergence when B^-1 Λ is symmetric. The benefits of this method are the well-conditioned linear systems produced and the ability to treat multiple or nearly degenerate eigenvalues.