Now showing items 1-5 of 5
Ritz Value Localization for Non-Hermitian Matrices
Rayleigh-Ritz eigenvalue estimates for Hermitian matrices obey Cauchy interlacing, which has helpful implications for theory, applications, and algorithms. In contrast, few results about the Ritz values of non-Hermitian ...
Short-Term Recurrence Krylov Subspace Methods for Nearly-Hermitian Matrices
The Progressive GMRES algorithm, introduced by Beckermann and Reichel in 2008, is a residual-minimizing short-recurrence Krylov subspace method for solving a linear system in which the coefficient matrix has a low-rank ...
The Stability of GMRES Convergence, with Application to Approximate Deflation Preconditioning
How does GMRES convergence change when the coefficient matrix is perturbed? Using spectral perturbation theory and resolvent estimates, we develop simple, general bounds that quantify the lag in convergence such a perturbation ...
Reconstructing an Even Damping from a Single Spectrum
We consider the wave equation on a finite interval with fixed ends and nonuniform viscous damping. We prove that the spectrum of the associated damped wave operator uniquely determines an even damping. We then develop a ...
Spectral Properties of Schrödinger Operators Arising in the Study of Quasicrystals
We survey results that have been obtained for self-adjoint operators, and especially Schrödinger operators, associated with mathematical models of quasicrystals. After presenting general results that hold in arbitrary ...