Accurate solution of structured linear systems via rank-revealing decompositions

@article{Dopico2012AccurateSO,
  title={Accurate solution of structured linear systems via rank-revealing decompositions},
  author={F. Dopico and J. M. Molera},
  journal={Ima Journal of Numerical Analysis},
  year={2012},
  volume={32},
  pages={1096-1116}
}
Linear systems of equations Ax = b, where the matrix A has some particular structure, arise frequently in applications. Very often structured matrices have huge condition numbers κ(A) = ‖A−1‖‖A‖ and, therefore, standard algorithms fail to compute accurate solutions of Ax = b. We say in this paper that a computed solution x is accurate if ‖x− x‖/‖x‖ = O(u), being u the unit roundoff. In this work, we introduce a framework that allows to solve accurately many classes of structured linear systems… Expand
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