18,988 research outputs found
On the Convergence of Ritz Pairs and Refined Ritz Vectors for Quadratic Eigenvalue Problems
For a given subspace, the Rayleigh-Ritz method projects the large quadratic
eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar
to the Rayleigh-Ritz method for the linear eigenvalue problem, the
Rayleigh-Ritz method defines the Ritz values and the Ritz vectors of the QEP
with respect to the projection subspace. We analyze the convergence of the
method when the angle between the subspace and the desired eigenvector
converges to zero. We prove that there is a Ritz value that converges to the
desired eigenvalue unconditionally but the Ritz vector converges conditionally
and may fail to converge. To remedy the drawback of possible non-convergence of
the Ritz vector, we propose a refined Ritz vector that is mathematically
different from the Ritz vector and is proved to converge unconditionally. We
construct examples to illustrate our theory.Comment: 20 page
BRDFs acquired by directional radiative measurements during EAGLE and AGRISAR
Radiation is the driving force for all processes and interactions between earth surface and atmosphere. The amount of
measured radiation reflected by vegetation depends on its structure, the viewing angle and the solar angle. This angular
dependence is usually expressed in the Bi-directional Reflectance Distribution Function (BRDF). This BRDF is not
only different for different types of vegetation, but also different for different stages of the growth. The BRDF therefore
has to be measured at ground level before any satellite imagery can be used the calculate surface-atmosphere
interaction. The objective of this research is to acquire the BRDFs for agricultural crop types.
A goniometric system is used to acquire the BRDFs. This is a mechanical device capable of a complete hemispherical
rotation. The radiative directional measurements are performed with different sensors that can be attached to this
system. The BRDFs are calculated from the measured radiation.
In the periods 10 June - 18 June 2006 and 2 July - 10 July 2006 directional radiative measurements were performed at
three sites: Speulderbos site, in the Netherlands, the Cabauw site, in the Netherlands, and an agricultural test site in
Goermin, Germany. The measurements were performed over eight different crops: forest, grass, pine tree, corn, wheat,
sugar beat and barley. The sensors covered the spectrum from the optical to the thermal domain. The measured radiance
is used to calculate the BRDFs or directional thermal signature.
This contribution describes the measurements and calculation of the BRDFs of forest, grassland, young corn, mature
corn, wheat, sugar beat and barley during the EAGLE2006 and AGRISAR 2006 fieldcampaigns. Optical BRDF have
been acquired for all crops except barley. Thermal angular signatures are acquired for all the crop
Momentum Kick Model Description of the Ridge in (Delta-phi)-(Delta eta) Correlation in pp Collisions at 7 TeV
The near-side ridge structure in the (Delta phi)-(Delta eta) correlation
observed by the CMS Collaboration for pp collisions at 7 TeV at LHC can be
explained by the momentum kick model in which the ridge particles are medium
partons that suffer a collision with the jet and acquire a momentum kick along
the jet direction. Similar to the early medium parton momentum distribution
obtained in previous analysis for nucleus-nucleus collisions at 0.2 TeV, the
early medium parton momentum distribution in pp collisions at 7 TeV exhibits a
rapidity plateau as arising from particle production in a flux tube.Comment: Talk presented at Workshop on High-pT Probes of High-Density QCD at
the LHC, Palaiseau, May 30-June2, 201
BDGS: A Scalable Big Data Generator Suite in Big Data Benchmarking
Data generation is a key issue in big data benchmarking that aims to generate
application-specific data sets to meet the 4V requirements of big data.
Specifically, big data generators need to generate scalable data (Volume) of
different types (Variety) under controllable generation rates (Velocity) while
keeping the important characteristics of raw data (Veracity). This gives rise
to various new challenges about how we design generators efficiently and
successfully. To date, most existing techniques can only generate limited types
of data and support specific big data systems such as Hadoop. Hence we develop
a tool, called Big Data Generator Suite (BDGS), to efficiently generate
scalable big data while employing data models derived from real data to
preserve data veracity. The effectiveness of BDGS is demonstrated by developing
six data generators covering three representative data types (structured,
semi-structured and unstructured) and three data sources (text, graph, and
table data)
Dependence of quantum correlations of twin beams on pump finesse of optical parametric oscillator
The dependence of quantum correlation of twin beams on the pump finesse of an
optical parametric oscillator is studied with a semi-classical analysis. It is
found that the phase-sum correlation of the output signal and idler beams from
an optical parametric oscillator operating above threshold depends on the
finesse of the pump field when the spurious pump phase noise generated inside
the optical cavity and the excess noise of the input pump field are involved in
the Langevin equations. The theoretical calculations can explain the previously
experimental results, quantitatively.Comment: 27 pages, 8 figure
On Inner Iterations in the Shift-Invert Residual Arnoldi Method and the Jacobi--Davidson Method
Using a new analysis approach, we establish a general convergence theory of
the Shift-Invert Residual Arnoldi (SIRA) method for computing a simple
eigenvalue nearest to a given target and the associated eigenvector.
In SIRA, a subspace expansion vector at each step is obtained by solving a
certain inner linear system. We prove that the inexact SIRA method mimics the
exact SIRA well, that is, the former uses almost the same outer iterations to
achieve the convergence as the latter does if all the inner linear systems are
iteratively solved with {\em low} or {\em modest} accuracy during outer
iterations. Based on the theory, we design practical stopping criteria for
inner solves. Our analysis is on one step expansion of subspace and the
approach applies to the Jacobi--Davidson (JD) method with the fixed target
as well, and a similar general convergence theory is obtained for it.
Numerical experiments confirm our theory and demonstrate that the inexact SIRA
and JD are similarly effective and are considerably superior to the inexact
SIA.Comment: 20 pages, 8 figure
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