Gauss Seidel is a iterative method to solve a system of equations. When using this method the initial matrix is decomposed into equations. Values are then guessed and checked, over the course of a few iterations these guesses are refined into the correct values.
Our source matrices:
To equations:
Make our initial guess of
We can then use the values we received and preform the process again.
Gauss Seidel on Wikipedia and ME 2004 Class Notes.
Example from sideserve, 06.14.21