Sparse matrix multiplication on vector computers
Abstract
An important kernel of scientific software is the multiplication of a sparse matrix by a vector. The efficiency of the algorithm on a vector computer depends on the storage scheme. With a storage by rows, performances are limited in general by the small vector length. Therefore a storage by so-called generalized colums has been designed, which provides long vectors and consequently good performances. However, it is not adapted to the symmetric case. A new type of storage, by sparse diagonals, has then been defined. It still exhibits long vectors, with performances as good as previously, but it is also well-suited to symmetric matrices. Results on a Cray2, with various sparse matrices, compare the three algorithms, and show the efficiency of the storage by sparse diagonale.