Fast parallel algorithms for solving triangular systems of linear equations on the hypercube

Presents efficient hypercube algorithms for solving triangular systems of linear equations by using various matrix partitioning and mapping schemes. Recently, several parallel algorithms have been developed for this problem. In these algorithms, the triangular solver is treated as the second stage of Gauss elimination. Thus, the triangular matrix is distributed by columns (or rows) in a wrap fashion since it is likely that the matrix is distributed this way after an LU decomposition has been done on the matrix. However, the efficiency of the algorithms is low. The motivation here is to develop various data partitioning and mapping schemes for hypercube algorithms by treating the triangular solver as an independent problem. Performance of the algorithms is analyzed theoretically and empirically by implementing them on a commercially available hypercube