Here is a question not specifically about the book, but I thought it might be appropriate in a numerical methods forum (if not here, where?).

I am writing an article about various numerical routines, including the computation of eigenvalues and eigenvectors. I would like to include in my article some examples from the real world.

So . . .
If you are computing eigenvalues, and don't mind sharing, please post back and let me know what kind of application is resulting in an eigensystem and how you are using the results.

Sincerely,


David

I would like to include in my article some examples from the real world.


I have encountered them in the solutions of systems of differential equations. One example from "A First Course in Differential Equations" 8th Edition by Dennis G. Zill is Project 8 - Designing for Earthquakes. When I was in school we were assigned this project and basically it consists of describing a three story building as a collection of springs with a forcing function (the earthquake) acting on the structure.

The equation is this.

M*X'' = K*X + F(t)

where M is the mass matrix, K is the stiffness matrix, F(t) is the forcing function, X'' is the acceleration matrix, and X is the displacment matrix.

The system can be re-written in this form.

X'' = A*X+M^-1*F(t)

where A = M^-1*X

If the forcing function, F(t) is zero the eigenvalues of A provide the natural frequencies of the building.

Hope that helps.

EDIT: In heat transfer they can be found is in the solution to the Graetz-Nusselt problem. (Among other places.)

http://www.springerlink.com/content/p765281007175q8q/

END EDIT:

Thanks
Matt