# 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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