@article{Alicja Smoktunowicz_Jakub Kierzkowski_Iwona Wróbel_2016, title={Forward Stability of Iterative Refinement with a Relaxation for Linear Systems}, volume={3}, url={https://www.avantipublishers.com/index.php/jaacm/article/view/834}, DOI={10.15377/2409-5761.2016.03.02.1}, abstractNote={<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>}, number={2}, journal={Journal of Advances in Applied & Computational Mathematics}, author={Alicja Smoktunowicz and Jakub Kierzkowski and Iwona Wróbel}, year={2016}, month={Dec.}, pages={68–73} }