Sparse matrix–vector multiplication

{{Short description|Computation routine}}

Sparse matrix–vector multiplication (SpMV) of the form {{math|1=y = Ax}} is a widely used computational kernel existing in many scientific applications. The input matrix {{mvar|A}} is sparse. The input vector {{mvar|x}} and the output vector {{mvar|y}} are dense. In the case of a repeated {{math|1=y = Ax}} operation involving the same input matrix {{mvar|A}} but possibly changing numerical values of its elements, {{mvar|A}} can be preprocessed to reduce both the parallel and sequential run time of the SpMV kernel.{{cite web | url=http://epubs.siam.org/doi/abs/10.1137/100813956 | title=Hypergraph Partitioning Based Models and Methods for Exploiting Cache Locality in Sparse Matrix-Vector Multiplication | accessdate=13 April 2014}}