Block Jacobi Preconditioning for Solving Dynamic General Equilibrium Models

Abstract

We apply preconditioning to improve computation of perfect foresight competitive equilibrium for the global economy with multiple production sectors and regions. The model is solved by an iterative method of the Gauss-Seidel type. At each iteration, first intertemporal variables are updated, and then equations for intratemporal variables are solved using the Newton-Krylov method. The Jacobian matrix of the system of equations for intra-temporal variables is close to the block diagonal part over regions. The inverse of this diagonal part is used as the preconditioner to speed up convergence of the Krylov method at each nonlinear iteration. The application of the block Jacobi preconditioning is illustrated in the example of the integrated Population-Economy-Technology-Science (iPETS) model.