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Gaia is an ambitious space mission of the European Space Agency which will chart a three-dimensional map the Milky Way to study the composition formation and evolution of our Galaxy. Our research team is developing the AVU-GSR verification module, aiming to obtain a reconstruction of the celestial sphere using a subset of GAIA observations. The authors propose a hybrid solution for HPC and Grid-MPI infrastructures which utilizes a modified LSQR - a conjugate gradient-based algorithm - to solve the system of equations for the sphere reconstruction. The proposed solution has been selected as pilot test for porting HPC applications in Grid.