The classical Rayleigh quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. Cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature.

Most existing works on riddling assume that the underlying dynamical system possesses an invariant subspace that usually results from a symmetry. In realistic applications of chaotic systems, however, there exists no perfect symmetry. The aim of this paper is to examine the consequences of symmetry-breaking on riddling. In particular, we consider smooth deterministic perturbations that destroy ...

The performance of Krylov subspace eigenvalue algorithms for large matrices can be measured by the angle between a desired invariant subspace and the Krylov subspace. We develop general bounds for this convergence that include the effects of polynomial restarting and impose no restrictions concerning the diagonalizability of the matrix or its degree of nonnormality. Associated with a desired se...

In the setting of operators on Hilbert spaces, we prove that every quasinilpotent operator has a non-trivial closed invariant subspace if and only pair idempotents with commutator common subspace. We also present geometric characterization subspaces classify are essentially idempotent.

In a previous paper, we found an extension of the N -dimensional Lorentz generators that partially restores the closed operator algebra in the presence of a Maxwell field, and is conserved under system evolution. Generalizing the construction found by Bérard, Grandati, Lages and Mohrbach for the angular momentum operators in the O(3)-invariant nonrelativistic case, we showed that the constructi...