a coarse-grained parallel QR-factorization algorithm for sparse least squares problems

摘要

A sparse QR-factorization algorithm SPARQR for coarse-grained parallel computations is described. the coefficient matrix, which is assumed to be general sparse, is reordered in an attempt to bring as many zero elements in the lower left corner as possible. The reordered matrix is then partitioned into block rows, and Givens plane rotations are applied in each block-row. These are independent tasks and can be done in parallel. Row and column permutations are carried Out within the diagonal blocks in an attempt to preserve better the sparsity of the matrix.