Many numerical simulations in (bilinear) quantum control use the monotonically convergent Krotov algorithms (introduced by Tannor et al. [Time Dependent Quantum Molecular Dynamics (1992) 347-360]), Zhu and Rabitz [J. Chem. Phys. (1998) 385-391] or their unified form described in Maday and Turinici [J. Chem. Phys. (2003) 8191-8196]. In Maday et al. [Num. Math. (2006) 323-338], a time discretization which preserves the property of monotonicity has been presented. This paper introduces a proof of the convergence of these schemes and some results regarding their rate of convergence.
@article{M2AN_2007__41_1_77_0,
author = {Salomon, Julien},
title = {Convergence of the time-discretized monotonic schemes},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {41},
year = {2007},
pages = {77-93},
doi = {10.1051/m2an:2007008},
mrnumber = {2323691},
zbl = {1124.65059},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2007__41_1_77_0}
}
Salomon, Julien. Convergence of the time-discretized monotonic schemes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) pp. 77-93. doi : 10.1051/m2an:2007008. http://gdmltest.u-ga.fr/item/M2AN_2007__41_1_77_0/
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