Introduction Dynamical systems as numerical methods. Classical Numerical methods for Optimization and Properties. Brief Review of Differential Geometry. Lie-Groups and homogeneous spaces. Linearly Convergent Methods.
Gradient flows on Lie Groups and homogeneous spaces.
Double Bracket Flows. Line search Descent methods on Lie-groups. Pole placement and balancing for Symmetric systems. QR-algorithm for Symmetric matrices. Covariant differentitation and the Levi-Civita Connection.