arXiv:1512.04246 Abstract | arXiv Analytics

arXiv:1512.04246 [math.NA]Abstract References Reviews Resources

Numerical stability of iterative refinement with a relaxation for linear systems

Alicja Smoktunowicz, Jakub Kierzkowski, Iwona Wrobel

Published 2015-12-14Version 1

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.

Comments: 12 pages

Categories: math.NA

Subjects: 65F05, 65F10, 15A12

Keywords: numerical stability, wilkinsons iterative refinement, best choice, extends existing results, relaxation ir

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