  This study focuses on the performance of two classical dense linear algebra
algorithms, the LU and the QR factorizations, on multilevel hierarchical
platforms. We first introduce a new model called Hierarchical Cluster Platform
(HCP), encapsulating the characteristics of such platforms. The focus is set on
reducing the communication requirements of studied algorithms at each level of
the hierarchy. Lower bounds on communications are therefore extended with
respect to the HCP model. We then introduce multilevel LU and QR algorithms
tailored for those platforms, and provide a detailed performance analysis. We
also provide a set of numerical experiments and performance predictions
demonstrating the need for such algorithms on large platforms.
