Scaling, Preconditioning, and Superlinear Convergence in GMRES-Type Iterations - Kaporin, Igor (Matrix Methods: Theory, Algorithms And Applications, 2010)
A theoretical justification is found for several standard techniques related to ILU preconditioning, such as pre-scaling and pivot modification, with implications for practical implementation. An improved estimate for the reduction of the GMRES residual is obtained within the general framework of two-stage preconditioning. In particular, an estimate in terms of a conditioning measure of the scaled coefficient matrix and the Frobenius norm of the scaled ILU residual is presented.