A Parallel Ring Ordering Algorithm for E cient One-sided Jacobi SVD Computations

In this paper we give evidence to show that in one-sided Jacobi SVD computation the sorting of column norms in each sweep is very important. An e cient parallel ring Jacobi ordering for computing singular value decomposition is described. This ordering can generate n(n 1)=2 di erent index pairs and sort column norms at the same time. The one-sided Jacobi SVD algorithm using this parallel ordering converges in about the same number of sweeps as the sequential cyclic Jacobi algorithm. The issue of equivalence of orderings for one-sided Jacobi is also discussed. We show how an ordering which does not sort column norms into order may still perform e ciently as long as it can generate the same index pairs at the same step as one which does sorting. Some experimental results on a Fujitsu AP1000 are presented.