  Stability analysis of Wilkinson's iterative refinement with a relaxation
IR(omega) for solving linear systems is given. It extends existing results for
omega=1, i.e., for Wilkinson's iterative refinement. We assume that all
computations are performed in fixed (working) precision arithmetic. Numerical
tests were done in MATLAB to illustrate our theoretical results. A particular
emphasis is given on convergence of iterative refinement with a relaxation. Our
tests confirm that the choice omega=1 is the best choice from the point of
numerical stability.
