Numerical Solution of Large-Scale Nonlinear Algebraic Systems
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
Calculus, Linear Algebra, Numerical Analysis
P. Deuflhard; Newton Methods for
Nonlinear Problems. Affine Invariance and Adaptive Algorithms.
Berlin-Heidelberg-New York, 2004