On parallel implementation of the one-sided Jacobi algorithm for singular value decompositions

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. Two parallel Jacobi orderings are described. These orderings can generate n(n-1)/2 different index pairs and sort column norms at the same time. The one-sided Jacobi SVD algorithm using these parallel orderings converges in about the same number of sweeps as the sequential cyclic Jacobi algorithm. Some experimental results on a Fujitsu AP1000 are presented. The issue of equivalence of orderings is also discussed