Reducing Overhead in Sparse Hypermatrix Cholesky Factorization

The sparse hypermatrix storage scheme produces a recursive 2D partitioning of a sparse matrix. Data subblocks are stored as dense matrices. Since we are dealing with sparse matrices some zeros can be stored in those dense blocks. The overhead introduced by the operations on zeros can become really large and considerably degrade performance. In this paper, we present several techniques for reducing the operations on zeros in a sparse hypermatrix Cholesky factorization. By associating a bit to each column within a data submatrix we create a bit vector. We can avoid computations when the bitwise AND of their bit vectors is null. By keeping information about the actual space within a data submatrix which stores non-zeros (dense window) we can reduce both storage and computation.