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Exploiting sparse matrices for speed

From: Joza
Subject: Exploiting sparse matrices for speed
Date: Mon, 5 Nov 2012 13:59:26 -0800 (PST)

In light of another thread I had, I thought it might be good to start a more
general discussion on the topic. As I stated in the other thread, I had a
1000x1000 sparse matrix with 2 on the main-diagonal, and -1 and the upper
and lower sub diagonal. All other entries were zero. Using a Successive
Over-Relaxation method to solve this took FOREVER in my my
desired accuracy, hours.

Surely there are ways of exploiting such massive sparsity for faster
algorithms! I'd be shocked if there weren't  

So, what are the general methods? I'd love to learn some new tricks!

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