On the convergence of Hill's method

Hill's method is a means to numerically approximate spectra of linear differential operators with periodic coefficients. In this paper, we address different issues related to the convergence of Hill's method. We show the method does not produce any spurious approximations, and that for self-adjoint operators, the method converges in a restricted sense. Further, assuming convergence of an eigenvalue, we prove convergence of the associated eigenfunction approximation in the L2-norm. These results are not restricted to self-adjoint operators. Finally, for certain self-adjoint operators, we prove that the rate of convergence of Hill's method to the least eigenvalue is faster than any polynomial power.

• Type: Journal
• Year: 2010
• Where: MOC
• Authors: Christopher W. Curtis, Bernard Deconinck
• Keywords: Certain Self-adjoint Operators, Convergence, MOC 2010, Security Privacy, Self-adjoint Operators