Reference suggestion: eigenvalues of tridiagonal matrices I would like to ask for a reference on the problem of computing the eigenvalues/eigenvectors of tridiagonal matrices (not necessarily with constant diagonals). 

I have seen authors use continued fractions and generating functions. However, I have thus far been unable to really grasp the foundations of this idea. From what I can see, the idea is really to reduce it to a difference equations. Then, perhaps, my request is for a good book on difference equations. 
Moreover, is there any technique which is really of a broad scope; ie applicable to a broad range of problems.

Thank you all in advance,

Gabieel
I tried looking up this subject on Google and found this article that seems extremely relevant to your problem: Eigenvalues of Several Tridiagonal Matrices. This article uses symbolic calculus to compute eigenvalues (which I barely know a thing about; I'm not one who works with linear algebra) of multiple tridiagonal matrices. I believe this one should help you, I've skimmed through it.
I strongly recommend the paper "Eigenvalue computation in the 20th century" by Golub &amp; van der Vorst and the references therein.