  Gaussian belief propagation (GaBP) is an iterative message-passing algorithm
for inference in Gaussian graphical models. It is known that when GaBP
converges it converges to the correct MAP estimate of the Gaussian random
vector and simple sufficient conditions for its convergence have been
established. In this paper we develop a double-loop algorithm for forcing
convergence of GaBP. Our method computes the correct MAP estimate even in cases
where standard GaBP would not have converged. We further extend this
construction to compute least-squares solutions of over-constrained linear
systems. We believe that our construction has numerous applications, since the
GaBP algorithm is linked to solution of linear systems of equations, which is a
fundamental problem in computer science and engineering. As a case study, we
discuss the linear detection problem. We show that using our new construction,
we are able to force convergence of Montanari's linear detection algorithm, in
cases where it would originally fail. As a consequence, we are able to increase
significantly the number of users that can transmit concurrently.
