Intel® oneAPI Math Kernel Library

supports iterative sparse solvers (ISS) based on the reverse communication interface (RCI), referred to here as the RCI ISS interface. The RCI ISS interface implements a group of user-callable routines that are used in the step-by-step solving process of a symmetric positive definite system (RCI conjugate gradient solver, or RCI CG), and of a non-symmetric indefinite (non-degenerate) system (RCI flexible generalized minimal residual solver, or RCI FGMRES) of linear algebraic equations. This interface uses the general RCI scheme described in [Dong95].

See the Appendix A Linear Solvers Basics for discussion of terms and concepts related to the ISS routines.

The term

RCI

indicates that when the solver needs the results of certain operations (for example, matrix-vector multiplications), the user performs them and passes the result to the solver. This makes the solver more universal as it is independent of the specific implementation of the operations like the matrix-vector multiplication. To perform such operations, the user can use the built-in sparse matrix-vector multiplications and triangular solvers routines described in Sparse BLAS Level 2 and Level 3 Routines.

Table

"RCI CG Interface Routines"

lists the names of the routines, and describes their general use.

The

Intel® oneAPI Math Kernel Library

RCI ISS interface routines are normally invoked in this order:

Advanced users can change that order if they need it. Others should follow the above order of calls.

The following diagram indicates the typical order in which the RCI ISS interface routines are invoked.

See the code examples that use the RCI ISS interface routines to solve systems of linear equations in the

Intel® oneAPI Math Kernel Library

installation directory.