A Comparison of Methods for Determining the Time Step When Propagating with the Lanczos Algorithm

N. Mohankumar and Tucker Carrington
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N. Mohankumar: 40, DJ Nagar, Peelamedu 6410004, India
Tucker Carrington: Chemistry Department, Queen’s University, Kingston, ON K7L 3N6, Canada

Mathematics, 2019, vol. 7, issue 11, 1-9

Abstract: To use the short iterative Lanczos algorithm to solve the time-dependent Schroedinger equation, one must choose, for a given Lanczos space size, a time step. We compare the derivation of the well-known Lubich and Hochbruck time step from SIAM J. Numer. Anal. 34 (1997) 1911 with the a priori time step we proposed in Mohankumar and Carrington (MC) Comput. Phys. Commun., 181 (2010) 1859 and demonstrate that the MC time step is somewhat larger, i.e., that the MC error bound is tighter. In addition, we use the MC approach to derive an error bound and time step for imaginary time propagation. The error bound we derive is much tighter than the error bound of Stewart and Leyk.

Keywords: short iterative Lanczos algorithm; propagation; Chebyshev error bounds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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