This work deals with the investigation of the performance of parallel iterative algorithms, used for the solution of linear systems obtained from the discretization of Elliptic PDEs using the Finite Element Collocation method. To increase parallelicity the initial matrix is reordered and then the algorithm is mapped on a distributed memory parallel computer. The case of the Star architecture with master-slave communication of the processors is studied. Earlier work of the authors is improved here and at the same time a new solution approach is developed so that the application of these iterative algorithms on more general problems is feasible. Speedup, processor utilization and efficiency measures are presented. The theoretical optimum is almost reached even though fixed number of processors was available.