Parallel Algorithms for Large Scale Macroeconometric Models

Macroeconometric models with forward-looking variables give raise to very large systems of equations that requires heavy computations. These models was influenced by the development of new and efficient computational techniques and they are an interesting testing ground for the numerical methods addressed in this research. The most difficult problem in solving such models is to obtain the solution of the linear system that arises during the Newton step. For this purpose we have used both direct methods based on matrix factorization and nonstationary iterative methods, also called Krylov methods that provide an interesting alternative to the direct methods. In this paper we present performance results of both serial and parallel versions of the algorithms involved in solving these models. Although parallel implementation of the most dense linear algebra operations is a well understood process, the availability of general purpose, high performance parallel dense linear algebra libraries is limited by the complexity of implementation. This paper describes PLSS – (Parallel Linear System Solver) a library which provides routines for linear system solving with an interface easy to use, that mirrors the natural description of sequential linear algebra algorithms.