So imagine I have been given the question as follows.
ax + by + cz = k [row 01]
dx + ey + fz = l [row 02]
gx + hy + iz = m [row 02]
Now if I solve this....the values converge to a certain value. But what if the rows 2 and 3 were switched and the values don't converge but go to some other values? Is my solution wrong in the second instance assuming the question asks me to go upto say the third iteration?
Let the matrix be $A=(a_{ij})$.
The convergence criterion of this iterative method is that it needs to be diagonally dominant, i.e.,$ | a_{ii} | > | a_{ij}| $ for all distinct pairs of $(i,j)$.
You can use elementary row swapping operations to rearrange the rows of matrix , so that the dominant term in each row is at the diagonal position.