One solves for the N component unknown vector u given the nonsingular coefficient matrix A and the N component right-hand side vector b . While these subroutines are not designed as production software, they should successfully handle industrial problems of moderate size, that is, ones that fit in high-speed memory.
All methods are available with adaptive parameter estimation and automatic stopping tests.
A switch to compute, if possible, the red-black indexing, permute the linear system, and permute associated vectors is provided. The successful convergence of iterative methods may be dependent on conditions that are difficult to determine in advance. For example, determining whether the coefficient matrix is positive definite can be as costly to check as solving the system. On the other hand, some conditions affecting convergence, such as positive diagonal elements, diagonal dominance, and symmetry are relatively easy to verify. For some applications, the theory may not exist to guarantee the convergence of an iterative method.