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.