PhD Course 2009

An Introduction to Pseudospectra and their Applications

Lecture 3

The program for the third day is as follows:

Questions and answers. Review of results on pseudospectra obtained last time. Review slides are here.
Further results on pseudospectra. I will cover pages 19-20 and example 6.4, pages 24-26, from the notes, in detail. Then I will explain how to define functions of a matrix. This covers pages 14 and 15 in the notes.
Coffee break.
Exercises, see below.
Lecture on the properties of norm(exp(tA)). Relation to spectrum, numerical range and pseudospectra. I will cover the material on pages 34-40 in the notes, although I will not talk about the proofs in detail. I hope to have time for some examples also.


Theoretical exercises

From the notes the following exercises:

Eigtool exercises

If you have not yet tried the various possibilities in eigtool (both the built-in demos and pseudospectra of matrices you define), now is the time to do so. From tomorrow I assume that you are familiar with the basics of this toolbox. Choose various matrices and experiment with them. Choose both normal and non-normal matrices as examples. I can provide suggestions for this part.

Further exercises using eigtool:

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Updated 15/09/2009, 12:55