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HSL_MP43 Sparse unsymmetric system: multiple-front method, equation entry

The module HSL_MP43 uses the multiple front method to solve sets of linear equations Ax = b (or AX = B) where A has been preordered to singly-bordered block-diagonal form

A11 C1 A22 C2 ANNCN .

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 (AllCL) separately. Thus, on each submatrix, L and U factors are computed. Once all possible eliminations have performed, for each submatrix there remains a frontal matrix Fl. The variables that remain in the front are called interface variables and the interface matrix F is formed by summing the matrices Fl. The interface matrix F 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.