Multilevel communication optimal LU and QR factorizations for hierarchical platforms

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 performance 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 communication 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 performance predictions showing the need for such algorithms on large platforms