# Sparse Matrices: Iterative Methods

Two routines employ iterative methods (as opposed to direct methods) for solving problems involving sparse matrices.

The IMSL_SP_GMRES function, based on the FORTRAN subroutine GMRESD by H. F. Walker, solves the linear system Ax = b using the GMRES method. This method is described in detail by Saad and Schultz (1986) and Walker (1988).

The IMSL_SP_CG function solves the symmetric definite linear system Ax = b using the conjugate gradient method with optional preconditioning. This method is described in detail by Golub and Van Loan (1983, chapter 10), and in Hageman and Young (1981, chapter 7).

- IMSL_SP_GMRES—Restarted generalized minimum residual (GMRES) method.
- IMSL_SP_CG—Conjugate gradient method.