  The Helmholtz equation arises in many applications, such as seismic and
medical imaging. These application are characterized by the need to propagate
many wavelengths through an inhomogeneous medium. The typical size of the
problems in 3D applications precludes the use of direct factorization to solve
the equation and hence iterative methods are used in practice. For higher
wavenumbers, the system becomes increasingly indefinite and thus good
preconditioners need to be constructed. In this note we consider an accelerated
Kazcmarz method (CGMN) and present an expression for the resulting iteration
matrix. This iteration matrix can be used to analyze the convergence of the
CGMN method. In particular, we present a Fourier analysis for the method
applied to the 1D Helmholtz equation. This analysis suggests an optimal choice
of the relaxation parameter. Finally, we present some numerical experiments.
