What's the benefit of solving a diagonally dominant matrix compared to an ordinary one?

Question

I have two linear systems of equations. One is strictly diagonal dominant and other is just an ordinary matrix. Both of them could have a very large scale. I'm wondering the benefit of solving a strictly diagonally dominant matrix compared to an ordinary one? What are the efficient techniques for both the types of matrix? And what are the possible problems?

Answer 1

For a strictly diagonal dominant matrix you don't need any permutations while computing an $LR$ factorisation, for bigger matrices you may use something like the jacobi methods, there you know it converges when the spectrum of $(I-D^{-1} A)$ is lower than 1.

When taking gauß-seidels methods it will always converge when it is strictly diagonal dominant.