Constructing Arrangements Optimally in Parallel.
Cet article constitue une présentation unifiée des principales méthodes de construction du treillis de Galois d'une correspondance. Nous rappelons d'abord sa définition, puis nous décrivons quatre algorithmes de construction des éléments du treillis qui sont les rectangles maximaux de la relation binaire. Ces algorithmes ne sont pas originaux. Les descriptions précises de algorithmes, le plus souvent absentes des publications originales, permettent une programmation simple, dans un langage procédural...
The convergence behavior of (1 +, λ)-ES is investigated at parabolic ridge, sharp ridge, and at the general case of the ridge functions. The progress rate, the distance to the ridge axis, the success rate, and the success probability are used in the analysis. The strong dependency of the (1 + λ)-ES to the initial conditions is shown using parabolic ridge test function when low distances to the ridge axis are chosen as the start value. The progress rate curve and the success probability curve of...
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...