The module HSL_MP43 uses the multiple front method to solve sets of linear equations (or ) where has been preordered to singly-bordered block-diagonal form
The HSL routines MA42 and MA52 are used with MPI for message passing.
In the multiple front method, a partial frontal decomposition is performed on each of the submatrices separately. Thus, on each submatrix, and factors are computed. Once all possible eliminations have performed, for each submatrix there remains a frontal matrix . The variables that remain in the front are called interface variables and the interface matrix is formed by summing the matrices . The interface matrix is also factorized using the frontal method. Block back-substitution completes the solution.
The matrix data and/or the matrix factors are optionally held in direct-access ﬁles.