Sparse matrix–vector multiplication

Sparse matrix-vector multiplication (SpMV) of the form $y=Ax$ is a widely used computational kernel existing in many scientific applications. The input matrix $A$ is sparse. The input vector $x$ and the output vector $y$ are dense. In the case of a repeated $y=Ax$ operation involving the same input matrix $A$ but possibly changing numerical values of its elements, $A$ can be preprocessed to reduce both the parallel and sequential run time of the SpMV kernel.