28,205 research outputs found
Closed orbit correction at synchrotrons for symmetric and near-symmetric lattices
This contribution compiles the benefits of lattice symmetry in the context of
closed orbit correction. A symmetric arrangement of BPMs and correctors results
in structured orbit response matrices of Circulant or block Circulant type.
These forms of matrices provide favorable properties in terms of computational
complexity, information compression and interpretation of mathematical vector
spaces of BPMs and correctors. For broken symmetries, a nearest-Circulant
approximation is introduced and the practical advantages of symmetry
exploitation are demonstrated with the help of simulations and experiments in
the context of FAIR synchrotrons
Convergence Analysis of Ensemble Kalman Inversion: The Linear, Noisy Case
We present an analysis of ensemble Kalman inversion, based on the continuous
time limit of the algorithm. The analysis of the dynamical behaviour of the
ensemble allows us to establish well-posedness and convergence results for a
fixed ensemble size. We will build on the results presented in [26] and
generalise them to the case of noisy observational data, in particular the
influence of the noise on the convergence will be investigated, both
theoretically and numerically. We focus on linear inverse problems where a very
complete theoretical analysis is possible
Improved coupled perturbed Hartree–Fock and Kohn–Sham convergence acceleration
A derivative version of the well-known direct inversion in the iterative subspace (DIIS) algorithm is presented. The method is used to solve the coupled perturbed Hartree–Fock (CPHF) equation to obtain the first and second derivatives of the density matrix with respect to an external electric field which, in this case, leads to the electric molecular polarizability and hyperpolarizability. Some comparisons are presented and the method shows good convergences in almost all cases
Well Posedness and Convergence Analysis of the Ensemble Kalman Inversion
The ensemble Kalman inversion is widely used in practice to estimate unknown
parameters from noisy measurement data. Its low computational costs,
straightforward implementation, and non-intrusive nature makes the method
appealing in various areas of application. We present a complete analysis of
the ensemble Kalman inversion with perturbed observations for a fixed ensemble
size when applied to linear inverse problems. The well-posedness and
convergence results are based on the continuous time scaling limits of the
method. The resulting coupled system of stochastic differential equations
allows to derive estimates on the long-time behaviour and provides insights
into the convergence properties of the ensemble Kalman inversion. We view the
method as a derivative free optimization method for the least-squares misfit
functional, which opens up the perspective to use the method in various areas
of applications such as imaging, groundwater flow problems, biological problems
as well as in the context of the training of neural networks
- …