In my maths course we are covering matrix permutations and bandwidth for example the (reverse) Cuthil McKee algorithm for re arranging a matrix into the (reverse) arrowhead form.
I am having trouble grasping an intuitive understanding into why we would want to do this and how it follows from LU decomposition? What are the implications of a large / small matrix bandwidth and why would we want to rearrange to get an arrow head adjacency matrix?
Edit I understand a smaller bandwidth is achieved from an arrowhead permutation but I'm not sure how this helps when solving a system.