Comparative analysis of approaches to hardware acceleration for sparse-matrix factorization

The authors compare two standard approaches to sparse LU (lower-upper) factorization, namely the compiled-code approach and the scatter-gather approach, with respect to three criteria that are relevant in the context of multiprocessor hardware acceleration: idealized parallelism, memory access costs, and storage requirements. The compiled-code approach was shown to be the clear winner with respect to the first metric, while the scatter-gather approach had much lower memory access cost and storage requirements. The use of a data structure in which rows of the sparse matrix are stored in an overlapped fashion along with the representation of a row-level operation as a single task was then proposed as a good compromise solution. The idealized parallelism with this approach was shown to be between that of the previous two approaches; its memory access cost was the same as with the scatter-gather approach, while its storage requirement was seen to be only moderately worse