wip/spai 3.2nb1 NetBSD

Given a sparse matrix A the SPAI Algorithm computes a sparse approximate inverse M by minimizing || AM - I || in the Frobenius norm. The approximate inverse is computed explicitly and can then be applied as a preconditioner to an iterative method.The sparsity pattern of the approximate inverse is either fixed a priori or captured automatically:

* Fixed sparsity: The sparsity pattern of M is either banded or a subset of the sparsity pattern of A. * Adaptive sparsity: The algorithm proceeds until the 2-norm of each column of AM-I is less than eps. By varying eps the user controls the quality and the cost of computing the preconditioner. Usually the optimal eps lies between 0.5 and 0.7.

A very sparse preconditioner is very cheap to compute but may not lead to much improvement, while if M becomes rather dense it becomes too expensive to compute. The optimal preconditioner lies between these two extremes and is problem and computer architecture dependent. The approximate inverse M can also be used as a robust (parallel) smoother for (algebraic) multi-grid methods