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,