We study the problem of minimizing non-linear trace quotient trace(V^TG(V)V)/trace(V^TH(V)V) over Stiefel manifold all n x p matrices with orthonormal columns. Hereby we assume G(V) and H(V) to be symmetric positive definite for V. In this way generalize robust Rayleigh optimization introduced by Bai et al. in article "Robust rayleigh minimization nonlinear eigenvalue problems". show a possible...

After reviewing the harmonic Rayleigh–Ritz approach for the standard and generalized eigenvalue problem, we discuss different extraction processes for subspace methods for the polynomial eigenvalue problem. We generalize the harmonic and refined Rayleigh–Ritz approach, which are new approaches to extract promising approximate eigenpairs from a search space. We give theoretical as well as numeri...

For standard eigenvalue problems, closed-form expressions for the condition numbers of a multiple eigenvalue are known. In particular, they are uniformly 1 in the Hermitian case and generally take different values in the non-Hermitian case. We consider the generalized eigenvalue problem and identify the condition numbers. Our main result is that a multiple eigenvalue generally has multiple cond...