Multigrid Methods in Economics

I present a self-contained introduction to multigrid methods with an emphasis on techniques relevant to dynamic programming problems. A probabilistic interpretation of the numerical principles is highlighted. Multigrid solvers are shown to be naturally matched to the challenges posed by intractable structural dynamic models routinely encountered in applied work. I argue that multigrid techniques have potential to substantially extend the scale and complexity of models under consideration. While most techniques in this paper can be found in other sources, their probabilistic interpretation and application to economics appear to be original