Solving Laplace equation iteratively

Hi,

I was given a task to solve Laplace equation for electrostatic potential (a 2D approximation, so without z component).

After some mathematical transormations it looks like this:

where U is represented by a given matrix:

I am supposed to solve this iteratively along this equation:

while setting boundary conditions in each step imposed by the presence of conductors with a fixed potential.

I know only basic calculation in Matlab, and never worked with such complex equation before. I know I'm asking a lot, but can anyone help me?