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
Freitag, M. A., & Spence, A. (2008). Rayleigh quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves. Linear Algebra and its Applications, 428(8-9), 2049-2060. https://doi.org/10.1016/j.laa.2007.11.013