PhD Course 2009

An Introduction to Pseudospectra and their Applications

Lecture 4

The program for the fourth day is as follows:

08:30-09:00

Questions and answers. Review of some results from yesterday.

09:00-10:00

Examples concerning the behavior of norm(exp(tA)) for small, intermediate, and large values of t.

10:00-10:20

Coffee break.

10:20-11:00

Exercises, see below.

11:10-12:00

Results on the behavior of norm(Aⁿ) for n large. I will cover results from pages 41-43 in the notes.

Exercises

Today you should familiarize yourselves with the entry in the Transients menu in Eigtool called 'Matrix Exponentiation', and also the two entries concerning bounds. I will give examples before the exercises, and propose matrices for numerical experiments.