TY - JOUR AU - Alicja Smoktunowicz, AU - Jakub Kierzkowski, AU - Iwona Wróbel, PY - 2016/12/30 Y2 - 2024/03/29 TI - Forward Stability of Iterative Refinement with a Relaxation for Linear Systems JF - Journal of Advances in Applied & Computational Mathematics JA - J. Adv. App. Comput. Math. VL - 3 IS - 2 SE - Articles DO - 10.15377/2409-5761.2016.03.02.1 UR - https://www.avantipublishers.com/index.php/jaacm/article/view/834 SP - 68-73 AB - <p> Stability analysis of Wilkinson’s iterative refinement method IR(<em>ω</em>) with a relaxation parameter <em>ω</em> for solving linear systems is given. It extends existing results for <em>ω</em>=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 <em>MATLAB</em> 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(<em>ω</em>) was given in [11]. Our opinion is opposite to that given in [11], since our experiments show that the choice <em>ω</em>=1 is the best choice from the point of numerical stability.</p> ER -