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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 },
pages = {77--93},
publisher = {EDP-Sciences},
volume = {41},
number = {1},
year = {2007},
doi = {10.1051/m2an:2007008},
mrnumber = {2323691},
zbl = {1124.65059},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007008/}
}
TY - JOUR AU - Salomon, Julien TI - Convergence of the time-discretized monotonic schemes JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2007 SP - 77 EP - 93 VL - 41 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007008/ DO - 10.1051/m2an:2007008 LA - en ID - M2AN_2007__41_1_77_0 ER -
%0 Journal Article %A Salomon, Julien %T Convergence of the time-discretized monotonic schemes %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2007 %P 77-93 %V 41 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007008/ %R 10.1051/m2an:2007008 %G en %F M2AN_2007__41_1_77_0
Salomon, Julien. Convergence of the time-discretized monotonic schemes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 1, pp. 77-93. doi: 10.1051/m2an:2007008
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