Visualizing sparse matrix computations

A description is given of ideas and tools that help with the visualization of sparse matrix computations. The Sparse Matrix Manipulation System, an environment for handling sparse matrices of all types in a flexible manner via ASCII file interfaces, is used. Two commands in this environment are ShowMatrix and ShowTree. The first illustrates the pattern of nonzeroes of a sparse matrix. The second illustrates dependencies among matrix elements. Other tools in the package are described, including tools for ordering, factoring and multiplying sparse matrices. This software environment is then used to study the effect of several recent ordering and partitioning algorithms for working with the sparse inverses of L and U. These new algorithms have been proposed as a means of enhancing the parallelism of sparse matrix computations. The effect of these algorithms on parallelism and fill-in is illustrated in a graphic manner