24 research outputs found
Robust Mean Square Stability of Open Quantum Stochastic Systems with Hamiltonian Perturbations in a Weyl Quantization Form
This paper is concerned with open quantum systems whose dynamic variables
satisfy canonical commutation relations and are governed by quantum stochastic
differential equations. The latter are driven by quantum Wiener processes which
represent external boson fields. The system-field coupling operators are linear
functions of the system variables. The Hamiltonian consists of a nominal
quadratic function of the system variables and an uncertain perturbation which
is represented in a Weyl quantization form. Assuming that the nominal linear
quantum system is stable, we develop sufficient conditions on the perturbation
of the Hamiltonian which guarantee robust mean square stability of the
perturbed system. Examples are given to illustrate these results for a class of
Hamiltonian perturbations in the form of trigonometric polynomials of the
system variables.Comment: 11 pages, Proceedings of the Australian Control Conference, Canberra,
17-18 November, 2014, pp. 83-8
Joint unmixing-deconvolution algorithms for hyperspectral images
International audienceThis paper combines supervised linear unmixing and deconvolution problems to increase the resolution of the abundance maps for industrial imaging systems. The joint unmixing-deconvolution (JUD) algorithm is introduced based on the Tikhonov regularization criterion for offline processing. In order to meet the needs of industrial applications, the proposed JUD algorithm is then extended for online processing by using a block Tikhonov criterion. The performance of JUD is increased by adding a non-negativity constraint which is implemented in a fast way using the quadratic penalty method and fast Fourier transform. The proposed algorithm is then assessed using both simulated and real hyperspectral images
Efficient Approaches for Enclosing the United Solution Set of the Interval Generalized Sylvester Matrix Equation
In this work, we investigate the interval generalized Sylvester matrix
equation and develop some
techniques for obtaining outer estimations for the so-called united solution
set of this interval system. First, we propose a modified variant of the
Krawczyk operator which causes reducing computational complexity to cubic,
compared to Kronecker product form. We then propose an iterative technique for
enclosing the solution set. These approaches are based on spectral
decompositions of the midpoints of , , and
and in both of them we suppose that the midpoints of and
are simultaneously diagonalizable as well as for the midpoints of
the matrices and . Some numerical experiments are given to
illustrate the performance of the proposed methods
The automatic solution of partial differential equations using a global spectral method
A spectral method for solving linear partial differential equations (PDEs)
with variable coefficients and general boundary conditions defined on
rectangular domains is described, based on separable representations of partial
differential operators and the one-dimensional ultraspherical spectral method.
If a partial differential operator is of splitting rank , such as the
operator associated with Poisson or Helmholtz, the corresponding PDE is solved
via a generalized Sylvester matrix equation, and a bivariate polynomial
approximation of the solution of degree is computed in
operations. Partial differential operators of
splitting rank are solved via a linear system involving a block-banded
matrix in operations. Numerical
examples demonstrate the applicability of our 2D spectral method to a broad
class of PDEs, which includes elliptic and dispersive time-evolution equations.
The resulting PDE solver is written in MATLAB and is publicly available as part
of CHEBFUN. It can resolve solutions requiring over a million degrees of
freedom in under seconds. An experimental implementation in the Julia
language can currently perform the same solve in seconds.Comment: 22 page
Two-sided Grassmann-Rayleigh quotient iteration
The two-sided Rayleigh quotient iteration proposed by Ostrowski computes a
pair of corresponding left-right eigenvectors of a matrix . We propose a
Grassmannian version of this iteration, i.e., its iterates are pairs of
-dimensional subspaces instead of one-dimensional subspaces in the classical
case. The new iteration generically converges locally cubically to the pairs of
left-right -dimensional invariant subspaces of . Moreover, Grassmannian
versions of the Rayleigh quotient iteration are given for the generalized
Hermitian eigenproblem, the Hamiltonian eigenproblem and the skew-Hamiltonian
eigenproblem.Comment: The text is identical to a manuscript that was submitted for
publication on 19 April 200