Sparse matrix-vector multiplication (SpMV) is of singular importance in sparse linear algebra, which is an important issue in scientific computing and engineering practice. Much effort has been put into accelerating SpMV, and a few parallel solutions have been proposed. This paper focuses on a special type of SpMV, namely sparse quasi-diagonal matrix-vector multiplication (SQDMV). The sparse quasi-diagonal matrix is the key to solving many differential equations, and very little research has been done in this field. This paper discusses data structures and algorithms for SQDMV that are efficie...