(untitled) (Journal of Computational Mathematics, 2018)
We discuss the convergence property of the Lanczos method for solving a complex shifted Hermitian linear system (α I + H)x = f. By showing the colinear coefficient of two system's residuals, our convergence analysis reveals that under the condition Re(α)+ λ _min(H)>0, the method converges faster than that for the real shifted Hermitian linear system (Re(α) I+H)x=f. Numerical experiments verify such convergence property.