Error bounds from extra-precise iterative refinement

@article{Demmel2006ErrorBF,
  title={Error bounds from extra-precise iterative refinement},
  author={James Demmel and Yozo Hida and William Kahan and Xiaoye S. Li and Sonil Mukherjee and E. Jason Riedy},
  journal={ACM Trans. Math. Softw.},
  year={2006},
  volume={32},
  pages={325-351}
}
We present the design and testing of an algorithm for iterative refinement of the solution of linear equations where the residual is computed with extra precision. This algorithm was originally proposed in 1948 and analyzed in the 1960s as a means to compute very accurate solutions to all but the most ill-conditioned linear systems. However, two obstacles have until now prevented its adoption in standard subroutine libraries like LAPACK: (1) There was no standard way to access the higher… CONTINUE READING