The Helmholtz equation arises in many applications, such as seismic andmedical imaging. These application are characterized by the need to propagatemany wavelengths through an inhomogeneous medium. The typical size of theproblems in 3D applications precludes the use of direct factorization to solvethe equation and hence iterative methods are used in practice. For higherwavenumbers, the system becomes increasingly indefinite and thus goodpreconditioners need to be constructed. In this note we consider an acceleratedKazcmarz method (CGMN) and present an expression for the resulting iterationmatrix. This iteration matrix can be used to analyze the convergence of theCGMN method. In particular, we present a Fourier analysis for the methodapplied to the 1D Helmholtz equation. This analysis suggests an optimal choiceof the relaxation parameter. Finally, we present some numerical experiments.
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