I'm working with finite difference formulas to obtain a semianalytical
solution of partial differential equations, and in my problems is
usual to have tridiagonal matrices like:
where N is the dimension of the matrix. To obtain the semianalytic
solution of my PDEs I need the eigenvalues of this matrix which are
easily computed with standard software (Mathematica, Matlab, etc.).
But by chance (I swear, it was by trial and error) I also found that
the eigenvalues of this kind of matrices can be computed using the
I know how the eigenvalues are computed through the solution of the polynomial equation
but I don't realise how to arrive to the trigonometric solution. Can someone give me a proof or a reference of this observation?
P.S.: I'm a newby in this forum and I still have problems with my LaTeX style, sorry. I'll improve it in the future