## Version 1.1.0

22nd February 2005

Recent Changes

This routine finds an approximate inverse $$\mathbf{M}$$ of an $$n \times n$$ sparse unsymmetric matrix $$\mathbf{A}$$ by attempting to minimize the difference between $$\mathbf{AM}$$ and the identity matrix in the Frobenius norm. The process may be improved by first performing a block triangularization of $$\mathbf{A}$$ and then finding approximate inverses to the resulting diagonal blocks.
$\mathbf{y} = \mathbf{M} \mathbf{z} \qquad \mathrm{and} \qquad \mathbf{y} = \mathbf{M} ^ T \mathbf{z}.$
The principal use of such an approximate inverse is likely to be in preconditioning iterative methods for solving the linear system $$\mathbf{Ax} = \mathbf{b}$$.