English

Numerical stability of iterative refinement with a relaxation for linear systems

Numerical Analysis 2015-12-15 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1512.04246,
  title  = {Numerical stability of iterative refinement with a relaxation for linear systems},
  author = {Alicja Smoktunowicz and Jakub Kierzkowski and Iwona Wrobel},
  journal= {arXiv preprint arXiv:1512.04246},
  year   = {2015}
}

Comments

12 pages

R2 v1 2026-06-22T12:08:52.756Z