# Rayleigh quotient

1. Nov 20, 2005

### Tony11235

Use the Rayleight quotient to find a good approximation for the principal eigenvalue of the Sturm-Liouville problem.
$$u'' + (\lambda - x^2)u = 0$$
$$0 < x < 0$$
$$u(0) = u'(1) = 0$$
Any help?

2. Nov 21, 2005

### Tony11235

Nobody has any idea?

3. Nov 21, 2005

### neo143

http://gershwin.ens.fr/vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/ [Broken]

Last edited by a moderator: May 2, 2017
4. Nov 21, 2005

### Tony11235

Directions?

Back to the problem, I know that you multiply both sides by u, integrate by parts, and then solve for lambda, after that I'm stuck.

Last edited by a moderator: May 2, 2017