This document discusses a method for solving linear systems of equations called composition of clans. It involves decomposing the system into subgroups of related equations called clans, solving each clan separately, and then combining the solutions. This approach can provide speed-up when implemented in parallel on multiple computing nodes. The document provides examples and discusses software called ParAd that implements parallel composition of clans. It concludes that speed-ups of up to 180 times have been achieved on problems with this approach.