| Abstract |
This second talk develops the theoretical framework behind the interpretation of advanced iterative methods as elementary iterations on larger spaces. The main tool is an auxiliary-space framework, which recasts an iterative method for the original system as an equivalent, but more elementary, method for a suitably enlarged auxiliary system.
Within this framework, many methods that appear sophisticated on the original problem can be understood as simple iterations applied to auxiliary variables. In particular, multigrid and domain decomposition methods can be viewed as Jacobi- or Gauss--Seidel-type iterations for appropriate expanded systems. This provides a rigorous way to connect advanced solvers with elementary iterative principles and clarifies the algebraic structure underlying these methods. |
