Banded Solvers

S3L includes both a tridiagonal and a general banded linear solver.

The tridiagonal solver does not perform pivoting, so it should be used only for systems that are known to be stable, such as diagonally dominant tridiagonal systems.

The banded solver performs partial pivoting, so it exhibits better stability than the tridiagonal solvers.

Both solvers will perform optimally when the LHS arrays are block-distributed along their last axis, the RHS arrays are block-distributed along their first axis, and the same block size is used for both distributions.

The S3L_gen_trid_factor function is used to factor a tridiagonal system of equations, where the main diagonal, upper subdiagonal and lower subdiagonal are given in three S3L arrays, D, U, and L.

S3L_gen_trid_solve, is used to solve a tridiagonal system of equations whose RHS matrix is given in an S3L array B, using the factorization results from a previous call to S3L_gen_trid_factor.

The banded solvers have linear complexity and their interprocess communication requirements are not great. Consequently, these banded solvers can deliver performance on clusters of small nodes that is similar to what would be achieved on a single node with many CPUs.