A band preconditioner matrix coupled to an iterative approach based on the generalized minimal residual (GMRes) method is presented to determine the cumulative reaction probability (CRP) N(E). The CRP is calculated using the Seideman, Manthe and Miller Lanczos-based boundary condition method [J. Chem. Phys. 96 (1992) 4412; 99 (1993) 3411]. Using this basis adapted preconditioner, the iterative GMRes scheme is found to be more efficient than a direct method based on the LU decomposition. The efficiency of this approach is illustrated by calculating the CRP for the H + O-2 -> HO + O reaction, assuming zero total angular momentum. (c) 2005 Elsevier B.V. All rights reserved.