Singular value computations on a massively parallel machine

Consideration is given to the computation of the singular value decomposition (SVD) on the Connection Machine (CM). Brief descriptions are given of the *Lisp language and some typical matrix manipulating functions. Implementation details of various Jacobi-SVD algorithms on an 8192-processor CM are presented. For n×n matrices, where n⩽64, the methods compute the decomposition in time O(n) per sweep. It is shown that the Connection Machine offers a highly efficient programming environment for SVD computations. Common bottlenecks, such as processor synchronization and data partitioning, are absent. The SIMD (single instruction multiple data) architecture is simple to use, and only minimal attention needs to be paid to the actual hardware configuration. The one-to-one matrix element to processor map means that, on a 65536-processor model, there are enough physical processors for n×n SVD problems so long as n⩽256