Spring 2007,  Math  6425, CRN: 15516

Course Title: Approximation of Dynamical Systems 

Course Meeting Time:  TR 3:30pm-4:45pm

Instructor: Serkan Gugercin

Course Web-page: http://math.vt.edu/people/gugercin/Math6425.htm

The course will cover  topics related to approximation (model 
reduction) of dynamical systems represented by sets of coupled 
differential or difference equations. The goal is to generate a 
simpler dynamical system, i.e., one being represented by smaller 
number of differential/difference equations, that approximates the 
behavior of the original system well in certain norms. 

Most model reduction techniques can be represented as a projection. 
In this course we will look at  two main classes of projection-based 
model reduction:  (1) SVD-based model reduction  and 
(2) Interpolation (Krylov) based model reduction.

The first category is related to the optimal approximation of 
constant matrices in the 2-induced norm. Balanced Truncation and 
Optimal Hankel Norm Approximation are the two most common methods 
in the category.  Despite their appealing theoretical properties, 
the computational requirements associated with these methods make 
them impractical for true large-scale settings.

The second category, on the other hand, is connected to 
interpolation/Pade approximation.  Most common techniques in this 
category are the Arnoldi and Lanczos procedures, and the rational 
Krylov methods. Unlike the SVD-based methods, these methods enjoy 
a great computational efficiency, but in some cases might lack 
rigorous theoretical guarantees.

We will analyze both classes of methods in detail and present 
comparisons/similarities. If time allows, Proper Orthogonal 
Decomposition (yet another projection-based technique) will be 
discussed as well. Several examples from various science and 
engineering disciplines will be presented.

For more details, see the course web-page at 
http://math.vt.edu/people/gugercin/Math6425.htm