Rayleigh quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves (Q2479518)

The authors deal with a non-Hermitian eigenvalue problem. They prove that, supposing a Galerkin-Krylov solver is used in exact arithmetic, the inexact Rayleigh quotient iteration with altered preconditioners and the inexact simplified Jacobi-Davidson method with the standard preconditioner provide equivalent approximate eigenvectors. Numerical examples are reported to enlighten this equivalence, which is motivated by theoretical reasons and applications.