I'm currently doing a little research into Multigrid methods, for future projects in Image/Video processing.
Amused by how much Multigrid improves over blind iteration, here's a sample, of a 1025 point solution X to the laplacian of a x being equal to 1, where x(0) = 0, x(1) = 1.
![[figure comparing multigrid results to
blind iterative results]](./mg-f1.jpg)
The red curve is remarkably close to ground truth. The green curve represents a solution found by blind Jacobi iteration (w = 2/3, the quasi-optimal weighting), after 131070 iterations. The blue curve is the result found by using multigrid, with only 64 iterations in total at each level.