In one of the previous slides, it showed that in order to calculate the new value at a particular point we needed to us all adjacent points. I am a little confused as to how each element is only dependent on the element to its left and up? Looking back at the slides it is hot completely obvious to me.

Given any iterations of the outer while loop, if we want to compute the value of A[i,j], we need the NEW values of A[i-1,j] and A[i,j-1] since they are updated in the same iteration. The values of A[i+1,j] and A[i,j+1] haven't been updated yet so they are still the OLD values from the previous iteration. Therefore, when we look for dependencies per iteration of the while loop, we only need to worry about A[i-1,j] and A[i,j-1] which are elements to the top and left.

What other methods are similar to Gauss-Seidel?