Block Course "GLOBAL NEWTON METHODS"


Speaker: Prof. Peter Deuflhard, the Founding Director of BISEC


Location: M842, Lecture Hall, Science Research Building M


Date & Time:

14:00-16:00, Oct. 24, 2017
14:00-16:00, Oct. 25, 2017
14:00-16:00, Oct. 27, 2017
14:00-16:00, Oct. 28, 2017
14:00-16:00, Oct. 30, 2017
10:00-12:00, Oct. 31, 2017
14:00-16:00, Nov. 1st, 2017
14:00-16:00, Nov. 3rd, 2017


Abstract:

1. Local Newton method

1.0. Introduction
1.1. Affin covariance - correction monotonicity
1.2. Affine contravariance - residual monotonicity
1.3. Adaptive numerical differenciation


2. Globalization by damping strategies

2.1. General level functions, Newton path
2.2. Natural level functions
2.3. Code NLEQ-ERR (NLEQ1)


3. Continuation methods (numerical pathfollowing)

3.1. Newton continuation methods
3.2. Gauss-Newton continuation method
3.3. Computation of bifurcation diagrams
3.4. Code ALCON


4. Quasi-Newton methods

4.1. Combination with Newton methods
4.2. Combination with Gauss-Newton continuation methods


5. Inexact Newton methods

5.1. Local convergence
5.2. Global convergence
5.3. Code GIANT-GBIT


6. Numerical comparisons of discrete PDEs