We show that for the non-Hermitian eigenvalue problem simplified Jacobi-Davidson with preconditioned Galerkin-Krylov solves is equivalent to inexact Rayleigh quotient iteration where the preconditioner is altered by a simple rank one change. This extends existing equivalence results to the case of preconditioned iterative solves. Numerical experiments are shown to agree with the theory.
- Inexact Rayleigh quotient iteration
- Nonsymmetric eigenproblem
- Eigenvalue approximation
- Iterative methods