Sparse QR factorization on a massively parallel computer

Abstract

This paper shows that QR factorization of large, sparse matrices can be performed efficiently on massively parallel SIMD (single instruction stream/multiple data stream) computers such as the Connection Machine CM-2. The problem is cast as a dataflow graph, whose nodes are mapped to a “virtual dataflow machine” in such a way that only nearest-neighbor communication is required. This virtual machine is implemented by programming the CM-2 processors to support a restricted dataflow protocol. Execution results for several test matrices show that good performance can be obtained without relying on nested dissection techniques.