Illustration of iterative linear solver behavior on simple 1D and 2D problems

Abstract: In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how classic linear solvers behave on this specific type of problems. For the sake of simplicity, we minimise either the squared gradient or the squared Laplacian, evaluated by finite differences on a regular 1D or 2D grid. We observed the evolution of the solution for both energies, in 1D and 2D, and with different solvers: Jacobi, Gauss-Seidel, SSOR (Symmetric successive over-relaxation) and CG (conjugate gradient [She94]). Plotting results at different iterations allows to have an intuition of the behavior of these classic solvers.