Dimensional analysis applied to a parallel QR algorithm

Abstract

We apply dimensional analysis to a formula for execution time for a QR algorithm from a paper by Henry and van de Geijn. We define a single efficiency surface that reduces performance analysis for this algorithm to an exercise in differential geometry. As the problem size and the number of processors change, different machines move along different paths on the surface determined by two computational forces specific to each machine. We show that computational force, also called computational intensity, is a unifying concept for understanding the performance of parallel numerical algorithms. © 2008 Springer-Verlag Berlin Heidelberg.