On the convergence of Hill’s method
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- by Christopher W. Curtis and Bernard Deconinck PDF
- Math. Comp. 79 (2010), 169-187 Request permission
Abstract:
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. Furthermore, assuming convergence of an eigenvalue, we prove convergence of the associated eigenfunction approximation in the $L^2$-norm. These results are not restricted to selfadjoint operators. Finally, for certain selfadjoint operators, we prove that the rate of convergence of Hill’s method to the least eigenvalue is faster than any polynomial power.References
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Additional Information
- Christopher W. Curtis
- Affiliation: Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-3420
- Email: curtchr@amath.washington.edu
- Bernard Deconinck
- Affiliation: Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-3420
- Received by editor(s): October 7, 2008
- Received by editor(s) in revised form: February 13, 2009
- Published electronically: July 6, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 79 (2010), 169-187
- MSC (2000): Primary 34L16, 65L07
- DOI: https://doi.org/10.1090/S0025-5718-09-02277-7
- MathSciNet review: 2552222