@misc{DeuflhardFreundWalter, author = {Deuflhard, Peter and Freund, R. and Walter, Artur}, title = {Fast Secant Methods for the Iterative Solution of Large Nonsymmetric Linear Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-330}, number = {SC-90-05}, abstract = {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 Broydens "good" and "bad" update techniques play a special role - but should be associated with two different line search principles. For Broydens "bad" update technique, a minimum residual principle is natural - thus making it theorectically comparable with a series of well-known algorithms like GMRES. Broydens "good" update technique, however, is shown to be naturally linked with a minimum "next correction" principle - which asymptotically mimics a minimum error principle. The two minimization principles differ significantly for sufficiently large system dimension. Numerical experiments on discretized PDE's of convection diffusion type in 2-D with internal layers give a first impression of the possible power of the derived "good" Broyden variant. {\bf Key Words:} nonsymmetric linear system, secant method, rank-1 update, Broydens method, line search, GMRES. AMS(MOS) {\bf Subject Classifications:} 65F10, 65N20.}, language = {en} } @article{DeuflhardFreundWalter1990, author = {Deuflhard, Peter and Freund, R. and Walter, Artur}, title = {Fast secant methods for the iterative solution of large nonsymmetric linear systems}, series = {IMPACT Comput. Sci. Eng.}, volume = {2}, journal = {IMPACT Comput. Sci. Eng.}, pages = {244 -- 276}, year = {1990}, language = {en} } @inproceedings{LedentsovJrKroppShchukinetal., author = {Ledentsov, Jr., Nikolay and Kropp, J{\"o}rg-R. and Shchukin, Vitaly and Steinle, Gunther and Ledentsov, Jr., Nikolay and Turkiewicz, Jarek P. and Wu, Bo and Shaofeng, Qiu and Ma, Yanan and Zhiyong, Feng and Burger, Sven and Schmidt, Frank and Caspar, Christoph and Freund, Ronald and Choquette, Kent D.}, title = {High-speed modulation, wavelength, and mode control in vertical-cavity surface-emitting lasers}, series = {Proc. SPIE}, volume = {9381}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2082951}, pages = {93810F}, language = {en} } @article{KoschekDurmazKrylovaetal., author = {Koschek, and Durmaz, Vedat and Krylova, and Wieczorek, and Gupta, Pooja and Richter, and Bujotzek, Alexander and Fischer, and Haag, Rainer and Freund, and Weber, Marcus and Rademann,}, title = {Peptide polymer ligands for a tandem WW-domain, a soft multivalent protein-protein interaction: lessons on the thermodynamic fitness of flexible ligands}, series = {Beilstein J. Org. Chem.}, volume = {11}, journal = {Beilstein J. Org. Chem.}, pages = {837 -- 847}, language = {en} }