José-Juan López-Espín
Universidad Miguel Hernández de Elche
Departamento de Estadística, matemáticas e Informática
Elche, 03202, Spain

Domingo Giménez
Universidad de Murcia, Spain
  
Solution of simultaneous equations systems by high performance methods

Keywords: simultaneous equations, parallel computing, lineal algebra libraries

Abstract: 
In some applications in econometrics it is necessary to solve simultaneous 
equations systems, which are made of thousands of equations and variables. 
One possibility is to solve this type of systems with some method which needs 
a lot of computational resources. On the other hand, it is also possible to 
solve the systems with a statistic method whose estimations are only 
approximations, with varying accuracy. Traditionally the second approach is 
used because no efficient software for high performance computers is available.
 In this work, the solution of symultaneous equations models by methods which 
demand the use of great computational resources is studied in high performance 
systems. The optimization of minimum square, two steps minimum square and 
iterative minimum square methods for present high performance systems is 
studied. The use of standard parallel computing software (OpenMP and MPI) and 
basic linear algebra libraries (BLAS, ATLAS and LAPACK) is considered. The 
solution of simultaneous equations systems with these routines and publicly 
available software is compared.