The GMRES polynomial solver manager can perform two types of linear solves. First the solver runs block GMRES, storing the resulting coefficients (or roots), which can be used to form a matrix polynomial. It then can reuse this polynomial as either a surrogate operator, or as a preconditioner for an outer solver. By applying the GMRES polynomial as an operator or preconditioner, one avoids the cost of the inner products and norms in GMRES, thus reducing communication costs.