Convergence of the time-discretized monotonic schemes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) no. 1, pp. 77-93.

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.

Classification : 49J20,  68W40
Mots clés : quantum control, monotonic schemes, optimal control, Łojasiewicz inequality
     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},
     pages = {77--93},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {1},
     year = {2007},
     doi = {10.1051/m2an:2007008},
     zbl = {1124.65059},
     mrnumber = {2323691},
     language = {en},
     url = {}
Salomon, Julien. Convergence of the time-discretized monotonic schemes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) no. 1, pp. 77-93. doi : 10.1051/m2an:2007008.

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