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

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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 $A x = b$ (or $A X = B$ ) where $A$ has been preordered to singly-bordered block-diagonal form

(\begin{matrix} A_{11} & C_{1} \\ A_{22} & C_{2} \\ \dots & \dots \\ \dots & \dots \\ A_{N N} & C_{N} \end{matrix}) .

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 $(A_{l l} C_{L})$ 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 $F_{l}$ . The variables that remain in the front are called interface variables and the interface matrix $F$ is formed by summing the matrices $F_{l}$ . 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.