The efficient solution of large sparse linear systems is critical for a wide range of applications. An important approach, considered here for the unsymmetric case, employs an iterative framework with a preconditioner. The preconditioners studied use a multilevel incomplete factorization, where incomplete means that the factors are approximate, with elements dropped to maintain sparsity. The details needed to understand algorithm features are well summarized, with ample references for the reader who is interested in greater depth.

A multitude of possibilities arise, including preprocessor choices for reducing fill-in and improving pivots, pivoting options, dropping rule details, and software selection. To make the study manageable, eight configurations are used that rely in part on software implementation default settings and focus on the important aspects of prepossessing and pivoting. Details of the software packages employed are outlined and related to the experimental comparisons. Problem dependence is effectively studied, using 12 areas from which 256 test matrices are extracted.

The performance profile approach provides an effective comparison of solution methods; the results are well presented, using graphs and tables. When selecting a method, it is important to know its sensitivity to the threshold parameter used for dropping. Results presented using a systematic approach related to the performance profile idea address this aspect. A table of recommendations is included that involves key considerations of available memory, threshold parameter knowledge, sparsity, and the important problem area. In some cases, a good sparse direct approach proves superior, but a preconditioned iterative method dominates for all memory-constrained cases considered.