Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem

Two different Lanczos-type methods for the linear response eigenvalue problem are analyzed. The first one is a natural extension of the classical Lanczos method for the symmetric eigenvalue problem while the second one was recently proposed by Tsiper specially for the linear response eigenvalue problem. Our analysis leads to bounds on errors for eigenvalue and eigenvector approximations by the two methods. These bounds suggest that the first method can converge significantly faster than Tsiper's method. Numerical examples are presented to support this claim.