no. 1
Convergence of the time-discretized monotonic schemes
ESAIM: 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.

DOI : 10.1051/m2an:2007008
Classification : 49J20, 68W40
Keywords: quantum control, monotonic schemes, optimal control, Łojasiewicz inequality 
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Salomon, Julien. Convergence of the time-discretized monotonic schemes. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 1, pp. 77-93. doi: 10.1051/m2an:2007008

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