In my recent post I motivated the elimination tree and gave a loose derivation from the cholesky task DAG. I thought it might be nice to visualize the actual tree computation algorithm (without path compression) to help develop intuition on how it represents fill-in in such a compact form. I asked codex to build this visualization which I share below:
Open the elimination tree visualization
You can step forwards or backwards in the elimination tree calculation. Fill-in entries get colored differently from starting nonzeros. You can see how when we traverse the partially constructed parents structure we can see the creation of new nonzeros.