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# 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} }

- Published 1990 in IMPACT Comput. Sci. Eng.
DOI:10.1016/0899-8248(90)90014-2

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