We survey numerical methods that are tractable in dynamic economic models with a finite, large number of continuous state variables. (Examples of such models are new Keynesian models, life-cycle models, heterogeneous-agents models, asset-pricing models, multisector models, multicountry models,...

First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions; this allows us to...