180 research outputs found
A variational derivation of a class of BFGS-like methods
We provide a maximum entropy derivation of a new family of BFGS-like methods.
Similar results are then derived for block BFGS methods. This also yields an
independent proof of a result of Fletcher 1991 and its generalisation to the
block case.Comment: 10 page
Time and spectral domain relative entropy: A new approach to multivariate spectral estimation
The concept of spectral relative entropy rate is introduced for jointly
stationary Gaussian processes. Using classical information-theoretic results,
we establish a remarkable connection between time and spectral domain relative
entropy rates. This naturally leads to a new spectral estimation technique
where a multivariate version of the Itakura-Saito distance is employed}. It may
be viewed as an extension of the approach, called THREE, introduced by Byrnes,
Georgiou and Lindquist in 2000 which, in turn, followed in the footsteps of the
Burg-Jaynes Maximum Entropy Method. Spectral estimation is here recast in the
form of a constrained spectrum approximation problem where the distance is
equal to the processes relative entropy rate. The corresponding solution
entails a complexity upper bound which improves on the one so far available in
the multichannel framework. Indeed, it is equal to the one featured by THREE in
the scalar case. The solution is computed via a globally convergent matricial
Newton-type algorithm. Simulations suggest the effectiveness of the new
technique in tackling multivariate spectral estimation tasks, especially in the
case of short data records.Comment: 32 pages, submitted for publicatio
Robust Steering of n-level Quantum Systems
Robust open-loop steering of a finite-dimensional quantum system is a central
problem in a growing number of applications of information engineering. In the
present paper, we reformulate the problem in the classical control-theoretic
setting, and provide a precise definition of {\em robustness} of the control
strategy. We then discuss and compare some significant problems from NMR in the
light of the given definition. We obtain quantitative results that are
consistent with the qualitative ones available in the physics literature.Comment: 10 page
- …