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 $\sigma$ 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 $\sigma$ 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