  Processes to automate the selection of appropriate algorithms for various
matrix computations are described. In particular, processes to check for, and
certify, various matrix properties of black box matrices are presented. These
include sparsity patterns and structural properties that allow "superfast"
algorithms to be used in place of black-box algorithms. Matrix properties that
hold generically, and allow the use of matrix preconditioning to be reduced or
eliminated, can also be checked for and certified - notably including in the
small-field case, where this presently has the greatest impact on the
efficiency of the computation.
