# 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(A
^{n}) 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.

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Updated 15/09/2009, 14:55