Fast secant methods for the iterative solution of large nonsymmetric linear systems

@article{Deuflhard1990FastSM,
  title={Fast secant methods for the iterative solution of large nonsymmetric linear systems},
  author={Peter Deuflhard and Roland Freund and Artur Walter},
  journal={IMPACT Comput. Sci. Eng.},
  year={1990},
  volume={2},
  pages={244-276}
}
A family of secant methods based on general rank-1 updates has been revisited in view of the construction of iterative solvers for large non-Hermitian linear systems. As it turns out, both Broy-den's "good" and "bad" update techniques play a special role — but should be associated with two different line search principles. For Broyden's "bad" update technique, a minimum residual principle is natural — thus making it theoretically comparable with a series of well-known algorithms like GMRES… CONTINUE READING

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