Numerical Solution of Large-Scale Nonlinear Algebraic Systems
Fall 2004

Prof. Dr. Ronald H.W. Hoppe


Large-scale nonlinear algebraic systems arise, for instance, from the discretization of differential and integral equations, in the framework of inverse problems as nonlinear least-squares problems, or as optimality conditions for nonlinear optimization problems. We will consider local and global Newton and Gauss-Newton methods and variants thereof. Emphasis will be put on a thorough affine invariant convergence analysis as well as on appropriate damping strategies and monotonicity tests for convergence monitoring. Compared to traditional approaches, the distinguishing affine invariance concept leads to shorter and more transparent proofs and permits the construction of adaptive algorithms. We will also address parameter dependent nonlinear problems and focus on path-following continuation methods for their numerical solution.


Calculus, Linear Algebra, Numerical Analysis


P. Deuflhard; Newton Methods for Nonlinear Problems.
Affine Invariance and Adaptive Algorithms. Springer, Berlin-Heidelberg-New York, 2004 (ISBN 3-540-21099-7)

Time table:
Tuesday 1:00 - 2:30 pm Room 315 PGH
Thursday 1:00 - 2:30 pm Room 315 PGH

Full Version


Prof. Dr. Ronald H.W. Hoppe
Office: 669 PGH
Phone: (713) 743-3452
Fax: (713) 743-3505