Fast Sparse Matrix-Vector Multiplication by Exploiting Variable Block Structure

Abstract. We improve the performance of sparse matrix-vector multiplication (SpMV) on modern cache-based superscalar machines when the matrix structure consists of multiple, irregularly aligned rectangular blocks. Matrices from finite element modeling applications often have this structure. We split the matrix, A, into a sum, A1 + A2 + . . . + As, where each term is stored in a new data structure we refer to as unaligned block compressed sparse row (UBCSR) format . A classical approach which stores A in a block compressed sparse row (BCSR) format can also reduce execution time, but the improvements may be limited because BCSR imposes an alignment of the matrix non-zeros that leads to extra work from filled-in zeros. Combining splitting with UBCSR reduces this extra work while retaining the generally lower memory bandwidth requirements and register-level tiling opportunities of BCSR. We show

• Type: Conference
• Year: 2005
• Where: HPCC
• Authors: Richard W. Vuduc, Hyun-Jin Moon
• Keywords: Extra Work, HPCC 2005, Sparse Matrix-vector Multiplication, Sparse Row