The Nonsingularity of Sparse Approximate Inverse Preconditioning and Its Performance Based on Processor Virtualization

In this paper, we analyze the properties of the sparse approximate inverse preconditioner, and prove that for a strictly diagonally dominant M matrix, the computed preconditioning matrix can be guaranteed to be nonsingular if it is nonnegative. Then we investigate the use of the processor virtualization technique to parallelize the sparse approximate inverse solver. Numerical experiments on a distributed memory parallel computer show that the efficiency of the resulting preconditioner can be improved by virtualization.

Kai Wang Orion Lawlor Laxmikant V. Kale, "The Nonsingularity of Sparse
 Approximate Inverse Preconditioning and Its Performance Based on Processor 
Virtualization", Parallel Programming Laboratory, Department of Computer Science, 
University of Illinois at Urbana-Champaign, 2005.