TY - GEN A1 - Deuflhard, Peter A1 - Freund, R. A1 - Walter, Artur T1 - Fast Secant Methods for the Iterative Solution of Large Nonsymmetric Linear Systems. N2 - 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. T3 - ZIB-Report - SC-90-05 KW - nonsymmetric linear systems KW - secant method KW - rank-1 update KW - Broyden's method KW - line search KW - GMRES Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-330 ER - TY - JOUR A1 - Deuflhard, Peter A1 - Freund, R. A1 - Walter, Artur T1 - Fast secant methods for the iterative solution of large nonsymmetric linear systems JF - IMPACT Comput. Sci. Eng. Y1 - 1990 VL - 2 SP - 244 EP - 276 ER - TY - CHAP A1 - Ledentsov, Jr., Nikolay A1 - Kropp, Jörg-R. A1 - Shchukin, Vitaly A1 - Steinle, Gunther A1 - Ledentsov, Jr., Nikolay A1 - Turkiewicz, Jarek P. A1 - Wu, Bo A1 - Shaofeng, Qiu A1 - Ma, Yanan A1 - Zhiyong, Feng A1 - Burger, Sven A1 - Schmidt, Frank A1 - Caspar, Christoph A1 - Freund, Ronald A1 - Choquette, Kent D. T1 - High-speed modulation, wavelength, and mode control in vertical-cavity surface-emitting lasers T2 - Proc. SPIE Y1 - 2015 U6 - https://doi.org/10.1117/12.2082951 VL - 9381 SP - 93810F ER - TY - JOUR A1 - Koschek, A1 - Durmaz, Vedat A1 - Krylova, A1 - Wieczorek, A1 - Gupta, Pooja A1 - Richter, A1 - Bujotzek, Alexander A1 - Fischer, A1 - Haag, Rainer A1 - Freund, A1 - Weber, Marcus A1 - Rademann, T1 - Peptide polymer ligands for a tandem WW-domain, a soft multivalent protein-protein interaction: lessons on the thermodynamic fitness of flexible ligands JF - Beilstein J. Org. Chem. Y1 - 2015 VL - 11 SP - 837 EP - 847 ER -