Biblio

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.