95,695 research outputs found
Fast algorithms for solving H∞-norm minimization problems
We propose an efficient computational approach to minimize the H ∞-norm of a transfer-function matrix depending affinely on a set of free parameters. The minimization problem, formulated as a semi-infinite convex programming problem, is solved via a relaxation approach over a finite set of frequency values. In this way, a significant speed up is achieved by avoiding the solution of high order LMIs resulting by equivalently formulating the minimization problem as a high dimensional semidefinite programming problem. Numerical results illustrate the superiority of proposed approach over LMIs based techniques in solving zero order H∞-norm approximation problems
Space-Time Isogeometric Analysis of Parabolic Evolution Equations
We present and analyze a new stable space-time Isogeometric Analysis (IgA)
method for the numerical solution of parabolic evolution equations in fixed and
moving spatial computational domains. The discrete bilinear form is elliptic on
the IgA space with respect to a discrete energy norm. This property together
with a corresponding boundedness property, consistency and approximation
results for the IgA spaces yields an a priori discretization error estimate
with respect to the discrete norm. The theoretical results are confirmed by
several numerical experiments with low- and high-order IgA spaces
Optimized Multi-Frequency Spectra for Applications in Radiative Feedback and Cosmological Reionization
The recent implementation of radiative transfer algorithms in numerous
hydrodynamics codes has led to a dramatic improvement in studies of feedback in
various astrophysical environments. However, because of methodological
limitations and computational expense, the spectra of radiation sources are
generally sampled at only a few evenly-spaced discrete emission frequencies.
Using one-dimensional radiative transfer calculations, we investigate the
discrepancies in gas properties surrounding model stars and accreting black
holes that arise solely due to spectral discretization. We find that even in
the idealized case of a static and uniform density field, commonly used
discretization schemes induce errors in the neutral fraction and temperature by
factors of two to three on average, and by over an order of magnitude in
certain column density regimes. The consequences are most severe for radiative
feedback operating on large scales, dense clumps of gas, and media consisting
of multiple chemical species. We have developed a method for optimally
constructing discrete spectra, and show that for two test cases of interest,
carefully chosen four-bin spectra can eliminate errors associated with
frequency resolution to high precision. Applying these findings to a fully
three-dimensional radiation-hydrodynamic simulation of the early universe, we
find that the HII region around a primordial star is substantially altered in
both size and morphology, corroborating the one-dimensional prediction that
discrete spectral energy distributions can lead to sizable inaccuracies in the
physical properties of a medium, and as a result, the subsequent evolution and
observable signatures of objects embedded within it.Comment: 15 pages, 13 figures, 2 tables, accepted for publication in the
Astrophysical Journa
On causal extrapolation of sequences with applications to forecasting
The paper suggests a method of extrapolation of notion of one-sided
semi-infinite sequences representing traces of two-sided band-limited
sequences; this features ensure uniqueness of this extrapolation and
possibility to use this for forecasting. This lead to a forecasting method for
more general sequences without this feature based on minimization of the mean
square error between the observed path and a predicable sequence. These
procedure involves calculation of this predictable path; the procedure can be
interpreted as causal smoothing. The corresponding smoothed sequences allow
unique extrapolations to future times that can be interpreted as optimal
forecasts.Comment: arXiv admin note: substantial text overlap with arXiv:1111.670
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