It is shown that square matrices A and B have a common invariant subspace W of dimension k > 1 if and only if for some scalar s, A + sI and B + sI are invertible and their kth compounds have a common eigenvector, which is a Grassmann representative for W . The applicability of this criterion and its ability to yield a basis for the common invariant subspace are investigated. © 2001 Elsevier Sci...

We present a general analytical model which describes the superlinear convergence of Krylov subspace methods. We take an invariant subspace approach, so that our results apply also to inexact methods, and to non-diagonalizable matrices. Thus, we provide a unified treatment of the superlinear convergence of GMRES, Conjugate Gradients, block versions of these, and inexact subspace methods. Numeri...

In Evans function computations of the spectra of asymptotically constant-coefficient linearized operators of large systems, a problem that becomes important is the efficient computation of global analytically varying bases for invariant subspaces of the limiting coefficient matrices. In the case that the invariant subspace is spectrally separated from its complementary invariant subspace, we pr...

A new algorithm is presented for computing primary decomposition of zero-dimensional ideals over finite fields. Like Berlekamp’s algorithm for univariate polynomials, the new method is based on the invariant subspace of the Frobenius map acting on the quotient algebra. The dimension of the invariant subspace equals the number of primary components, and a basis of the invariant subspace yields a...