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In this work we present two parallel algorithms for the solution of a given least squares problem with structured matrices. This problem arises in many applications most related to digital signal processing, an exam-ple is given. Both parallel algorithms have been designed to speed{up the sequential one in a heterogeneous network of computers. They dier from the approximation followed to implement parallel algorithms on heteroge-neous networks of computers known as HeHo and HoHe strategies. How-ever, our study goes beyond the practical usefulness of our heterogeneous parallel application. One one hand, the results obtained validates the recent developed HeteroMPI as a very useful tool for programming het-erogeneous parallel algorithms. On the other hand, although HeteroMPI has initially been designed to apply the HeHo strategy, we propose a way this tool can be used in the HoHe strategy. Pros and cons of the use of HeteroMPI for both strategies will be deeply study through the applica