A three-parameter fast Givens QR algorithm for superscalar processors

We present a three parameter fast Givens QR algorithm that exploits parallelism to improve performance on superscalar processors. We provide a selection of parameter values for which the new algorithm reduces to the standard algorithm, but show that non-standard values minimize the number of cache misses, memory references and pipeline stalls. Using a tractable model of a superscalar machine architecture, we derive rules for estimating the optimal combination of parameter values. Applying these rules, we observe a speedup over the standard algorithm of 2.4 on the Intel Pentium Pro system, 2.0 on a single thin POWER2 processor of the IBM SP2, 1.6 on a single wide POWER2 processor of the IBM SP2, and 4.2 on a single R8000 processor of the SGI POWER Challenge XL.