Direct and Transposed Sparse Matrix-Vector Multiplication

In this paper we investigate the execution of Ab and AT b, where A is a sparse matrix and b a dense vector, using the Blocked Based Compression Storage (BBCS) scheme and an Augmented Vector Architecture (AVA). In particular, we demonstrate that by using the BBCS format, we can represent both the direct and the transposed matrix for the purposes of matrix-vector multiplication with no additional costs in storage, access time and computation performance. To achieve this, we propose a new instruction and a hardware modification for the AVA. Subsequently we evaluate the performance of the transposed Sparse Matrix Vector Multiplication (SMVM) and demonstrate that like for the direct SMVM, the BBCS scheme outperforms other general schemes like the Jagged Diagonal (JD) and the Compressed Row Storage (CRS) by 1.7 to 4.1 times. Furthermore we show that the BBCS scheme outperforms CRS and JD when the aforementioned SMVM is used in the Conjugate Gradient and Bi-Conjugate Gradient iterative solve algorithms for which speedups of 1.78 to 4.13 depending were achieved in simulations.