Could you tell me please, are there any analytical methods how to find eigenvalues of matrix such this one?

$$ \begin{pmatrix} a_1 & b_1 & 0 & 0 & 0 & \ldots & 0 \\ b_1 & a_2 & b_2 & 0 & 0 & \ldots & 0\\ 0 & b_2 & a_3 & b_3 & 0 & \ldots & 0 \\ 0&0 &b_3 & a_4&b_4 & \ldots & 0\\ \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & 0 & \ldots & a_{n-1} & b_{n-1}\\ 0 & 0 & 0& 0& \ldots & b_{n-1} & a_n \end{pmatrix} $$

I've found previously solutions for some special cases, but here all matrix elements are different and nonzero.