The particular iterative technique we want you to use in the assignment is called Jacobi iteration. The basic idea is that we can first guess at a solution for the values (the in our application). We can then determine how bad the guess is by calculating and seeing how far from 0 it is at each point. This difference is called the residual. The idea of the iterative technique is that we use this residual to improve our next guess of . In particular we use the iteration:
We keep repeating this step deriving new s until our error is small.
To make this work well we first need to adjust each row of the matrix so that the diagonal is . We can do this by multiplying each row and value by .