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{\large Melina A. Freitag \\
{\bf Rayleigh Quotient iteration and simplified Jacobi-Davidson method
with preconditioned iterative solves.
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 Dept. of Mathematical Sciences\\ 
 University of Bath\\
 Claverton Down \\
 Bath BA2 7AY, UK \\
{\tt m.freitag@maths.bath.ac.uk}\\
Alastair Spence
% goldfarb@columbia.edu
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We show that for the non-Hermitian eigenvalue problem simplified
Jacobi-Davidson with preconditioned iterative solves is equivalent to
inexact Rayleigh quotient iteration where the preconditioner is altered by
a simple rank change. This extends existing equivalence results to the
case of preconditioned iterative solves. Numerical experiments are shown
to agree with the theory.
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