A parameterized ordering for cache-, register- and pipeline-efficient Givens QR decomposition

Abstract

A parameterized ordering of Givens rotations and guidelines for choosing parameter values is presented in the context of QR decomposition. Although a standard selection of parameter values retrieves an ordering that corresponds to a well-known algorithm, we show that non-standard values decrease the execution time. We implement the new ordering on an Intel Pentium Pro system, a single thin POWER2 processor of the IBM SP2, and a single R8000 processor of the SGI POWER Challenge XL. On each machine, we observe performance that is more than twice that of the original ordering.