Optimized resolution of systems of equations

Abstract

Sparse systems of equations are an essential part of real mod- els, being decisive in simulation or optimization. By increasing the prob- lems size or going closer to reality, these systems increase in complexity and size. There are several proven methods to solve them e ciently, and it is known that a structural reorganization can enhance e ciency. We propose an improvement to the Extended Direct Method algorithm as a preprocessor of the adjacency matrix associated with the system. This method was originated in the Design of Chemical Plant Instrumentation, expanding the functions of its predecessor, the Direct Method, which did not take into account the degree of nonlinearity of model equations and variables.