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This paper presents an efficient technique for matrix-vector andvector-transpose-matrix multiplication in distributed-memory parallel computingenvironments, where the matrices are unstructured, sparse, and have asubstantially larger number of columns than rows or vice versa. Our methodallows for parallel I/O, does not require extensive preprocessing, and has thesame communication complexity as matrix-vector multiplies with column or rowpartitioning. Our implementation of the method uses MPI. We partition thematrix by individual nonzero elements, rather than by row or column, and use an"overlapped" vector representation that is matched to the matrix. The transposemultiplies use matrix-specific MPI communicators and reductions that we showcan be set up in an efficient manner. The proposed technique achieves a goodwork per processor balance even if some of the columns are dense, while keepingcommunication costs relatively low.

Efficient Distributed-Memory Parallel Matrix-Vector Multiplication with Wide or Tall Unstructured Sparse Matrices