Convergence of the time-discretized monotonic schemes

Julien Salomon

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 1, page 77-93
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Salomon, Julien. "Convergence of the time-discretized monotonic schemes." ESAIM: Mathematical Modelling and Numerical Analysis 41.1 (2007): 77-93. <http://eudml.org/doc/250026>.

@article{Salomon2007,
abstract = { 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. },
author = {Salomon, Julien},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Quantum control; monotonic schemes; optimal control; Ł ojasiewicz inequality.; quantum control; Lojasiewicz inequality; time discretization; Schrödinger equation; convergence},
language = {eng},
month = {4},
number = {1},
pages = {77-93},
publisher = {EDP Sciences},
title = {Convergence of the time-discretized monotonic schemes},
url = {http://eudml.org/doc/250026},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Salomon, Julien
TI - Convergence of the time-discretized monotonic schemes
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/4//
PB - EDP Sciences
VL - 41
IS - 1
SP - 77
EP - 93
AB - 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.
LA - eng
KW - Quantum control; monotonic schemes; optimal control; Ł ojasiewicz inequality.; quantum control; Lojasiewicz inequality; time discretization; Schrödinger equation; convergence
UR - http://eudml.org/doc/250026
ER -

References

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