I am looking for references on how to solve the generalized eigen-problem : $$Ax = \lambda Bx \tag{1}$$ Where $A$ is a symmetric matrix and $B$ is symmetric positive definite. I know a standard approach is to perform a Cholesky factorisation of $B$ and then to solve : $$L^{-1}AL^{-T}y = \lambda y \tag{2}$$ With $B = LL^T$, $y = L^T x$. And then to apply an implicitly restarted Lanczos (or Arnoldi) method.
I would like to know if it is possible to use an implicitly restarted (Generalized) Lancozs method directly to (1).