Forward Stability of Iterative Refinement with a Relaxation for Linear Systems

Stability analysis of Wilkinson’s iterative refinement method IR(ω) with a relaxation parameter ω for solving linear systems is given. It extends existing results for ω=1, i.e., for Wilkinson’s iterative refinement method. 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 method with a relaxation. A preliminary error analysis of the Algorithm IR(ω) was given in [11]. Our opinion is opposite to that given in [11], since our experiments show that the choice ω=1 is the best choice from the point of numerical stability