  We consider the Cauchy problem for the Helmholtz equation with a domain in
R^d, d>2 with N cylindrical outlets to infinity with bounded inclusions in
R^{d-1}. Cauchy data are prescribed on the boundary of the bounded domains and
the aim is to find solution on the unbounded part of the boundary. In 1989,
Kozlov and Maz'ya proposed an alternating iterative method for solving Cauchy
problems associated with elliptic,self-adjoint and positive-definite operators
in bounded domains. Different variants of this method for solving Cauchy
problems associated with Helmholtz-type operators exists. We consider the
variant proposed by Mpinganzima et al. for bounded domains and derive the
necessary conditions for the convergence of the procedure in unbounded domains.
For the numerical implementation, a finite difference method is used to solve
the problem in a simple rectangular domain in R^2 that represent a truncated
infinite strip. The numerical results shows that by appropriate truncation of
the domain and with appropriate choice of the Robin parameters, the
Robin-Dirichlet alternating iterative procedure is convergent.
