This applet demonstrates the Conjugate Gradient Method for approximating the solution to the Laplace Finite Difference Equation. A description of the Conjugate Gradient method and a related method called Steepest Descent is provided here

Finite difference cells that appear white indicate a value less than zero and cells that appear black represent values greater than 100. Compare the number of iterations required for the Conjugate Gradient Method to drive the maximum residual to zero (to five decimal places) with the iteration count for the Gauss Seidel and SOR Methods and Jacobi Method.