SAS/IML Software's Sparse Matrix Algorithms

SAS/IML software provides subroutines that implement iterative and direct algorithms for solving large sparse systems of linear equations of the form x=b, where A is a nonsingular square matrix. The ITSOLVER subroutine supports the following classes of iterative solvers:

Convergence of an iterative method depends upon the distribution of eigenvalues for the matrix A, and it can be rather slow for badly conditioned matrices. For such cases SAS/IML offers the following hybrid algorithms, which combine an incomplete factorization (a modified direct method) used in the preconditioning phase with an iterative refinement procedure:

The SOLVELIN subroutine supports the following direct sparse solvers for symmetric positive-definite systems: