# PhD Course 2009

## An Introduction to Pseudospectra and their Applications

### Lecture 5

The program for the fifth day is as follows:

- 08:30-09:00
- Questions and answers. Review of some results from
Friday September 18.
- 09:00-10:00
- Schur factorization and departure from
normality. Brief review of polynomial interpolation.
Introduction to spectral differentiation and
Chebyshev differentiation matrices. Part of the material
comes from section 10.2 in the lecture notes.
- 10:00-10:15
- Coffee break.
- 10:15-10:45
- More about Chebyshev differentiation matrices. Matlab examples.
- 10:45-12:00
- Exercises, see below.

#### Exercises

Theoretical exercises.

- Exercise 10.1.
- Exercise 10.2.

Matlab exercises.

- Experiment with the Chebyshev differentiation matrices and the
normalized Chebyshev differentiation matrices. The Chebyshev
differentiation matrix is generated using cheb.m, and the normalized
one using chebnor.m.

Webpages maintained by Arne Jensen, matarne at math.aau.dk

Updated 23/09/2009, 10:55