66,254 research outputs found
Structure Preserving Parallel Algorithms for Solving the Bethe-Salpeter Eigenvalue Problem
The Bethe-Salpeter eigenvalue problem is a dense structured eigenvalue
problem arising from discretized Bethe-Salpeter equation in the context of
computing exciton energies and states. A computational challenge is that at
least half of the eigenvalues and the associated eigenvectors are desired in
practice. We establish the equivalence between Bethe-Salpeter eigenvalue
problems and real Hamiltonian eigenvalue problems. Based on theoretical
analysis, structure preserving algorithms for a class of Bethe-Salpeter
eigenvalue problems are proposed. We also show that for this class of problems
all eigenvalues obtained from the Tamm-Dancoff approximation are overestimated.
In order to solve large scale problems of practical interest, we discuss
parallel implementations of our algorithms targeting distributed memory
systems. Several numerical examples are presented to demonstrate the efficiency
and accuracy of our algorithms
Optimization viewpoint on Kalman smoothing, with applications to robust and sparse estimation
In this paper, we present the optimization formulation of the Kalman
filtering and smoothing problems, and use this perspective to develop a variety
of extensions and applications. We first formulate classic Kalman smoothing as
a least squares problem, highlight special structure, and show that the classic
filtering and smoothing algorithms are equivalent to a particular algorithm for
solving this problem. Once this equivalence is established, we present
extensions of Kalman smoothing to systems with nonlinear process and
measurement models, systems with linear and nonlinear inequality constraints,
systems with outliers in the measurements or sudden changes in the state, and
systems where the sparsity of the state sequence must be accounted for. All
extensions preserve the computational efficiency of the classic algorithms, and
most of the extensions are illustrated with numerical examples, which are part
of an open source Kalman smoothing Matlab/Octave package.Comment: 46 pages, 11 figure
Dynamic Rate and Channel Selection in Cognitive Radio Systems
In this paper, we investigate dynamic channel and rate selection in cognitive
radio systems which exploit a large number of channels free from primary users.
In such systems, transmitters may rapidly change the selected (channel, rate)
pair to opportunistically learn and track the pair offering the highest
throughput. We formulate the problem of sequential channel and rate selection
as an online optimization problem, and show its equivalence to a {\it
structured} Multi-Armed Bandit problem. The structure stems from inherent
properties of the achieved throughput as a function of the selected channel and
rate. We derive fundamental performance limits satisfied by {\it any} channel
and rate adaptation algorithm, and propose algorithms that achieve (or
approach) these limits. In turn, the proposed algorithms optimally exploit the
inherent structure of the throughput. We illustrate the efficiency of our
algorithms using both test-bed and simulation experiments, in both stationary
and non-stationary radio environments. In stationary environments, the packet
successful transmission probabilities at the various channel and rate pairs do
not evolve over time, whereas in non-stationary environments, they may evolve.
In practical scenarios, the proposed algorithms are able to track the best
channel and rate quite accurately without the need of any explicit measurement
and feedback of the quality of the various channels.Comment: 19 page
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