Reconcile Large Multi-Regional Input-Output databases using Generalized Minimal Residual method  and fast computing

Abstract In the design of multi-regional input-output (Multi-RegionalInput-Output (MRIO)) databases, data has to be reconciled from several sources. This requires looking for an equilibrated MRIO table that fits data from each source. The performances of the current data reconciliation methods, which mostly use RAS-type algorithms, is quite constrained. Furthermore, the mathematical underpinnings of RAS-type algorithms are not fully understood, and they are limited in their ability to handle particular constraints. Some methods, like the Least-Squares and Chebychev, have been shown to have a solid mathematical foundation. Still, they come with extra complexity regarding the number of iterations and computation needs. This paper proposes the integration of the Generalized Minimal Residual Method to reconcile many data sources for the MRIO databases. The comparison of the Generalized MinimalResidual (GMRES)’s convergence with the availability centered inventory model (Availability Centered Inventory Model (ACIM)) method for reconciliation shows its rapidity and robustness. In addition, the results show the low complexity of the GMRES compared to other existing methods. Keywords: Multi-regional input-output (MRIO), Sustainability, ACIM method, GMRES method, Data Conciliation, System Resolution.