# Finding interior eigenvalues using Davidson algorithm

Is it possible to find interior eigenvalues closer to some lambda using Davidson method? I was searching online but found that most people use Jacobi-Davidson method for that.

• please refer to this paper. "Targeted excited state algorithms" – Izzy Vang Nov 24 '19 at 21:48
• Do you mean this paper? Can you write a brief description of why would this paper be useful to answer the question? Unfortunately, in the current form, this answer was not up to the standards of SE, so I converted it to a comment. Feel free to repost it as an answer @IzzyVang with a little more details. – Anton Menshov Nov 24 '19 at 22:03

Normally, Davidson adds the residuals from the lowest eigenvalue approximate solutions: $$K (A - \tilde \lambda_i I) \tilde v_i \quad : \quad i < n$$ where $K$ is the preconditioner (approximate inverse), $\tilde \lambda_i$ is an approximate eigenvalue, $\tilde v_i$ is the corresponding approximate eigenvector, $i$ sorts in ascending order, and $n$ is the number of desired eigenvectors. You would want to change the sorting to be by distance from your desired eigenvalue.