# 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.

Thanks

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.