# Sparse matrix-vector multiplication

Sparse matrix-vector multiplication (SpMV) of the form ${\displaystyle y=Ax}$ is a widely used computational kernel existing in many scientific applications. The input matrix ${\displaystyle A}$ is sparse. The input vector ${\displaystyle x}$ and the output vector ${\displaystyle y}$ are dense. In case of repeated ${\displaystyle y=Ax}$ operation involving the same input matrix ${\displaystyle A}$ but possibly changing numerical values of its elements, ${\displaystyle A}$ can be preprocessed to reduce both the parallel and sequential run time of the SpMV kernel.[1]