Version 1.1.0

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MI12 Unsymmetric system: approximate-inverse preconditioner

This routine finds an approximate inverse M of an n × n sparse unsymmetric matrix A by attempting to minimize the difference between AM and the identity matrix in the Frobenius norm. The process may be improved by first performing a block triangularization of A and then finding approximate inverses to the resulting diagonal blocks.

A second entry allows the user to form the matrix-vector products

y = Mzandy = MTz.

The principal use of such an approximate inverse is likely to be in preconditioning iterative methods for solving the linear system Ax = b.