Forward Stability of Iterative Refinement with a Relaxation for Linear Systems


Iterative refinement, numerical stability, condition number.

How to Cite

Alicja Smoktunowicz, Jakub Kierzkowski, & Iwona Wróbel. (2016). Forward Stability of Iterative Refinement with a Relaxation for Linear Systems. Journal of Advances in Applied &Amp; Computational Mathematics, 3(2), 68–73.


 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.


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Copyright (c) 2016 Alicja Smoktunowicz, Jakub Kierzkowski, Iwona Wróbel