The Impact of Hardware Gather/Scatter on Sparse Gaussian Elimination

Recent vector supercomputers provide vector memory access to "randomly" indexed vectors, whereas early vector supercomputers required contiguously or regularly indexed vectors. This additional capability, known as "hardware gather/scatter," can be used to great effect in general sparse Gaussian elimination. In this note we present some examples that show the impact of this change in hardware on the choice of algorithms for sparse Gaussian elimination. Common folk wisdom holds that general sparse Gaussian elimination algorithms do not perform well on vector computers. Our numerical results demonstrate that hardware gather/scatter allows general sparse elimination algorithms to outperform algorithms based on a band, envelope, or block structure on such computers.