Partitioning Sparse Rectangular Matrices for Parallel Computations of Ax and ATv

Partitioning Sparse Rectangular Matrices for Parallel Processing?

We are interested in partitioning sparse rectangular matrices for parallel processing. The partitioning problem has been well-studied in the square symmetric case, but the rectangular problem has received very little attention. We will formalize the rectangular matrix partitioning problem and discuss several methods for solving it. We will extend the spectral partitioning method for symmetric m...

Partitioning Rectangular and Structurallynonsymmetric Sparse Matrices for Parallel

Partitioning Rectangular and Structurally Unsymmetric Sparse Matrices for Parallel Processing

A common operation in scientific computing is the multiplication of a sparse, rectangular, or structurally unsymmetric matrix and a vector. In many applications the matrix-transposevector product is also required. This paper addresses the efficient parallelization of these operations. We show that the problem can be expressed in terms of partitioning bipartite graphs. We then introduce several ...

Partitioned Sparse A-1 Methods

This paper solves the classic Ax=b problem by constructing factored components of the inverses of L and U, the triangular factors of A. The number of additional fill-ins in the partitioned inverses of L and U can be made zero. The number of partitions is related to the path length of sparse vector methods. Allowing some fill-in in the partitioned inverses of L and U results in fewer partitions....

Permuting Sparse Rectangular Matrices into Block-Diagonal Form

We investigate the problem of permuting a sparse rectangular matrix into blockdiagonal form. Block-diagonal form of a matrix grants an inherent parallelism for solving the deriving problem, as recently investigated in the context of mathematical programming, LU factorization, and QR factorization. To represent the nonzero structure of a matrix, we propose bipartite graph and hypergraph models t...