33.2. Matrix-Free methods

TAO fully supports matrix-free methods. The matrices specified in the Hessian evaluation routine need not be conventional matrices; instead, they can point to the data required to implement a particular matrix-free method. The matrix-free variant is allowed only when the linear systems are solved by an iterative method in combination with no preconditioning ( PCNONE or -pc_type none), a user-provided preconditioner matrix, or a user-provided preconditioner shell ( PCSHELL); that is, obviously matrix-free methods cannot be used if a direct solver is to be employed. Details about using matrix-free methods are provided in the PETSc Users Manual.