A parallel multisplitting solution of the least squares problem

Distributed Weighted Least-Squares and Gaussian Belief Propagation: An Integrated Approach

“…Finally, by solving (17) according to (4), we obtain the mean and variance set (x c k , vc k ) that corresponds to (14). After obtaining these marginals, the last step includes defining messages from variable nodes X tie c k to factor nodes F tie .…”

“…where xs and vs are obtained by solving (17). The mean z fi→xs and variance v fi→xs are calculated as defined in (11).…”

“…In every iteration, all clusters are updated (line 13) and WLS is computed over the clusters (line 14). Next, means and variances from tie variable nodes to tie factor nodes are calculated using the GBP (lines [15][16][17][18]. Upon the completion of previous lines, all means and variances from tie factor nodes to tie variable nodes can be calculated (lines [20][21][22][23][24][25].…”

“…In the next subsection, we propose different approach to solve the system of linear equations (17), alternative to solving the system in each iteration from the scratch (line 14). Note that for the system defined in (17), only vectors s c k and q c k dynamically change their values through iterations according to messages from tie factor nodes to tie variable nodes.…”

Distributed Weighted Least-Squares and Gaussian Belief Propagation: An Integrated Approach

“…wherex s andv s are obtained by solving (17). The mean z fi→xs and variance v fi→xs are calculated as defined in (11).…”