Junction tree algorithms for solving sparse linear systems
In this technical report we present a self-contained introduction to algorithms that solve sparse linear systems by message passing on a junction tree (a.k.a. clique tree). When solving the systemAx = b whereA is a sparse n×nmatrix, these methods require O(n · w3) time and O(n · w2) space, where w is the treewidth of A’s sparsity graph. These algorithms are useful for parallel or distributed solutions to linear systems, or to efficiently solve sets of similar linear systems.