1,176 research outputs found
Improved success rate and stability for phase retrieval by including randomized overrelaxation in the hybrid input output algorithm
In this paper, we study the success rate of the reconstruction of objects of
finite extent given the magnitude of its Fourier transform and its geometrical
shape. We demonstrate that the commonly used combination of the hybrid input
output and error reduction algorithm is significantly outperformed by an
extension of this algorithm based on randomized overrelaxation. In most cases,
this extension tremendously enhances the success rate of reconstructions for a
fixed number of iterations as compared to reconstructions solely based on the
traditional algorithm. The good scaling properties in terms of computational
time and memory requirements of the original algorithm are not influenced by
this extension.Comment: 14 pages, 8 figure
Fast Markov chain Monte Carlo sampling for sparse Bayesian inference in high-dimensional inverse problems using L1-type priors
Sparsity has become a key concept for solving of high-dimensional inverse
problems using variational regularization techniques. Recently, using similar
sparsity-constraints in the Bayesian framework for inverse problems by encoding
them in the prior distribution has attracted attention. Important questions
about the relation between regularization theory and Bayesian inference still
need to be addressed when using sparsity promoting inversion. A practical
obstacle for these examinations is the lack of fast posterior sampling
algorithms for sparse, high-dimensional Bayesian inversion: Accessing the full
range of Bayesian inference methods requires being able to draw samples from
the posterior probability distribution in a fast and efficient way. This is
usually done using Markov chain Monte Carlo (MCMC) sampling algorithms. In this
article, we develop and examine a new implementation of a single component
Gibbs MCMC sampler for sparse priors relying on L1-norms. We demonstrate that
the efficiency of our Gibbs sampler increases when the level of sparsity or the
dimension of the unknowns is increased. This property is contrary to the
properties of the most commonly applied Metropolis-Hastings (MH) sampling
schemes: We demonstrate that the efficiency of MH schemes for L1-type priors
dramatically decreases when the level of sparsity or the dimension of the
unknowns is increased. Practically, Bayesian inversion for L1-type priors using
MH samplers is not feasible at all. As this is commonly believed to be an
intrinsic feature of MCMC sampling, the performance of our Gibbs sampler also
challenges common beliefs about the applicability of sample based Bayesian
inference.Comment: 33 pages, 14 figure
Critical Slowing-Down in Landau Gauge-Fixing Algorithms
We study the problem of critical slowing-down for gauge-fixing algorithms
(Landau gauge) in lattice gauge theory on a -dimensional lattice. We
consider five such algorithms, and lattice sizes ranging from to
(up to in the case of Fourier acceleration). We measure four
different observables and we find that for each given algorithm they all have
the same relaxation time within error bars. We obtain that: the so-called {\em
Los Alamos} method has dynamic critical exponent , the {\em
overrelaxation} method and the {\em stochastic overrelaxation} method have , the so-called {\em Cornell} method has slightly smaller than
and the {\em Fourier acceleration} method completely eliminates critical
slowing-down. A detailed discussion and analysis of the tuning of these
algorithms is also presented.Comment: 40 pages (including 10 figures). A few modifications, incorporating
referee's suggestions, without the length reduction required for publicatio
The LHMC Algorithm for Free Field Theory: Reexamining Overrelaxation
We analyze the autocorrelations for the LHMC algorithm in the context of free
field theory. In this case this is just Adler's overrelaxation algorithm. We
consider the algorithm with even/odd, lexicographic, and random updates, and
show that its efficiency depends crucially on this ordering of sites when
optimized for a given class of operators. In particular, we show that, contrary
to previous expectations, it is possible to eliminate critical slowing down
(z[int]=0) for a class of interesting observables, including the magnetic
susceptibility: this can be done with lexicographic updates but is not possible
with even/odd (z[int]=1) or random (z[int]=2) updates. We are considering the
dynamical critical exponent z[int] for integrated autocorrelations rather than
for the exponential autocorrelation time; this is reasonable because it is the
integrated autocorrelation which determines the cost of a Monte Carlo
computation.Comment: LaTeX, 33 pages, 3 postscript figure
A comparison of updating algorithms for large N reduced models
We investigate Monte Carlo updating algorithms for simulating
Yang-Mills fields on a single-site lattice, such as for the Twisted
Eguchi-Kawai model (TEK). We show that performing only over-relaxation (OR)
updates of the gauge links is a valid simulation algorithm for the Fabricius
and Haan formulation of this model, and that this decorrelates observables
faster than using heat-bath updates. We consider two different methods of
implementing the OR update: either updating the whole matrix at once,
or iterating through subgroups of the matrix, we find the same
critical exponent in both cases, and only a slight difference between the two.Comment: 21 pages, 4 figure
Simulating the Electroweak Phase Transition in the SU(2) Higgs Model
Numerical simulations are performed to study the finite temperature phase
transition in the SU(2) Higgs model on the lattice. In the presently
investigated range of the Higgs boson mass, below 50 GeV, the phase transition
turns out to be of first order and its strength is rapidly decreasing with
increasing Higgs boson mass. In order to control the systematic errors, we also
perform studies of scaling violations and of finite volume effects.Comment: 46 pages with 16 figures, DESY-94-15
Biased Metropolis-Heat-Bath Algorithm for Fundamental-Adjoint SU(2) Lattice Gauge Theory
For SU(2) lattice gauge theory with the fundamental-adjoint action an
efficient heat-bath algorithm is not known so that one had to rely on
Metropolis simulations supplemented by overrelaxation. Implementing a novel
biased Metropolis-heat-bath algorithm for this model, we find improvement
factors in the range 1.45 to 2.06 over conventionally optimized Metropolis
simulations. If one optimizes further with respect to additional overrelaxation
sweeps, the improvement factors are found in the range 1.3 to 1.8.Comment: 4 pages, 2 figures; minor changes and one reference added; accepted
for publication in PR
The Electroweak Phase Transition: A Non-Perturbative Analysis
We study on the lattice the 3d SU(2)+Higgs model, which is an effective
theory of a large class of 4d high temperature gauge theories. Using the exact
constant physics curve, continuum () results for the
properties of the phase transition (critical temperature, latent heat,
interface tension) are given. The 3-loop correction to the effective potential
of the scalar field is determined. The masses of scalar and vector excitations
are determined and found to be larger in the symmetric than in the broken
phase. The vector mass is considerably larger than the scalar one, which
suggests a further simplification to a scalar effective theory at large Higgs
masses. The use of consistent 1-loop relations between 3d parameters and 4d
physics permits one to convert the 3d simulation results to quantitatively
accurate numbers for different physical theories, such as the Standard Model --
excluding possible nonperturbative effects of the U(1) subgroup -- for Higgs
masses up to about 70 GeV. The applications of our results to cosmology are
discussed.Comment: 69 pages, 48 figures as uuencoded compressed postscrip
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