Rounding error analysis of two-stage iterative methods for large linear systems

摘要

We study the finite precision behavior of two-stage iterative methods for solving a linear system Ax=b which is consistent in case A is singular, i.e., b∈R(A), the range of A. Using the rounding error analysis technique presented in [Accuracy and stability of numerical algorithms, SIAM, Philadelphia, PA, 1996] we deduce conditions under which a two-stage iterative method is forward stable or backward stable.