Sparse approximate-inverse preconditioners using norm-minimization techniques

We investigate the use of sparse approximate-inverse preconditioners for the iterative solution of unsymmetric linear systems of equations. We consider the approximations proposed by Cosgrove, Diaz, and Griewank [Internat. J. Comput. Math., 44 (1992), pp. 91-110] and Huckle and Grote [A New Approach to Parallel Preconditioning with Sparse Approximate Inverses, Tech. report SCCM-94-03, Stanford University, 1994] which are based on norm-minimization techniques. Such methods are of particular interest because of the considerable scope for parallelization. We propose a number of enhancements which may improve their performance. When run in a sequential environment, these methods can perform unfavorably when compared with other techniques. However, they can be successful when other methods fail and simulations indicate that they can be competitive when considered in a parallel environment.