# Gaussian Belief Propagation

A demonstration of the reweighted Gaussian belief propagation algorithm.
 Matrix Settings Matrix Properties Positive Definite Diagonally Dominant Matrix Size = 5 Belief Propagation Settings Initialization Simulation Speed Fast Slow Stopped Reweighting Parameter (c) = 15
Error:
Estimated Minimum:

# Description

The above is a demonstration of the Gaussian belief propagation (GaBP) algorithm with a reweighted message passing scheme. The GaBP algorithm is an iterative message-passing scheme that attempts to solve the linear system $$Ax = b$$ for the vector $$x$$ or, equivalently, GaBP attempts to minimize the quadratic $$-1/2x'Ax - h'x$$. Observe that for sufficiently large choices of the reweighting parameter, $$c$$, the computation trees produced by the algorithm are positive definite and the message updates are well-defined. When $$c = 1$$, and the matrix is scaled diagonally dominant (equivalently, walk-summable), then the algorithm always converges.