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Direction-preserving and Schur-monotonic Semi-separable Approximations of Symmetric Positive Definite Matrices

Description: For a given symmetric positive definite matrix A {element_of} R{sup nxn}, we develop a fast and backward stable algorithm to approximate A by a symmetric positive-definite semi-separable matrix, accurate to any prescribed tolerance. In addition, this algorithm preserves the product, AZ, for a given matrix Z {element_of} R{sup nxd}, where d << n. Our algorithm guarantees the positive-definiteness of the semi-separable matrix by embedding an approximation strategy inside a Cholesky factorization procedure to ensure that the Schur complements during the Cholesky factorization all remain positive definite after approximation. It uses a robust direction-preserving approximation scheme to ensure the preservation of AZ. We present numerical experiments and discuss potential implications of our work.
Date: October 20, 2009
Creator: Gu, Ming; Li, Xiaoye Sherry & Vassilevski, Panayot S.
Partner: UNT Libraries Government Documents Department

Bipartite graph partitioning and data clustering

Description: Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie recommender system. In this paper, the authors propose a new data clustering method based on partitioning the underlying biopartite graph. The partition is constructed by minimizing a normalized sum of edge weights between unmatched pairs of vertices of the bipartite graph. They show that an approximate solution to the minimization problem can be obtained by computing a partial singular value decomposition (SVD) of the associated edge weight matrix of the bipartite graph. They point out the connection of their clustering algorithm to correspondence analysis used in multivariate analysis. They also briefly discuss the issue of assigning data objects to multiple clusters. In the experimental results, they apply their clustering algorithm to the problem of document clustering to illustrate its effectiveness and efficiency.
Date: May 7, 2001
Creator: Zha, Hongyuan; He, Xiaofeng; Ding, Chris; Gu, Ming & Simon, Horst D.
Partner: UNT Libraries Government Documents Department

Results from the NSTX X-ray Crystal Spectrometer

Description: A high-resolution X-ray crystal spectrometer has recently been installed at the National Spherical Torus Experiment to record the satellite spectra of helium-like argon, ArXVII, in the wavelength range from 3.94 to 4.00 {angstrom} for measurements of ion and electron temperatures, and measurements of the ionization equilibrium of argon, which is of interest for studies of ion transport. The instrument presently consists of a spherically bent quartz crystal and a conventional one-dimensional position-sensitive multi-wire proportional counter, but it will soon be upgraded to a new type of X-ray imaging crystal spectrometer by the installation of a large size (10 cm x 30 cm) two-dimensional position-sensitive detector that will allow us to obtain temporally and spatially resolved spectra from an 80 cm high cross-section of the plasma. In its present configuration, the spectrometer has been optimized for high throughput so that it is possible to record spectra with small statistical errors with a time resolution of 10 ms by adding only small, nonperturbing amounts of argon to the plasma. The spectrometer is most valuable for measurements of the ion temperature in the absence of a neutral beam in ohmically heated and radio-frequency heated discharges, when charge exchange recombination spectroscopy does not function. Electron temperature measurements from the satellite-to-resonance line ratios have been important for a quantitative comparison with (and verification of) the Thomson scattering data. The paper will describe the instrumental details of the present and future spectrometer configurations, and present recent experimental results.
Date: January 14, 2003
Creator: Bitter, M.; Hill, K.; Roquemore, L.; Beiersdorfer, P.; Thorn, D. & Gu, Ming Feng
Partner: UNT Libraries Government Documents Department

Inner-Shell Absorption Lines of Fe 6-Fe 16: a Many-Body Perturbation Theory Approach

Description: We provide improved atomic calculation of wavelengths, oscillator strengths, and autoionization rates relevant to the 2 -> 3 inner-shell transitions of Fe VI-XVI, the so-called Fe M-shell unresolved transition array (UTA). A second order many-body perturbation theory is employed to obtain accurate transition wavelengths, which are systematically larger than previous theoretical results by 15-45 mA. For a few transitions of Fe XVI and Fe XV where laboratory measurements exist, our new wavelengths are accurate to within a few mA. Using these new calculations, the apparent discrepancy in the velocities between the Fe M-shell UTA and other highly ionized absorption lines in the outflow of NGC 3783 disappears. The oscillator strengths in our new calculation agree well with the previous theoretical data, while the new autoionization rates are significantly larger, especially for lower charge states. We attribute this discrepancy to the missing autoionization channels in the previous calculation. The increased autoionization rates may slightly affect the column density analysis of the Fe M-shell UTA for sources with high column density and very low turbulent broadening. The complete set of atomic data is provided as an electronic table.
Date: January 17, 2006
Creator: Gu, Ming F.; /KIPAC, Menlo Park; Holczer, Tomer; Behar, Ehud; /Technion; Kahn, Steven M. et al.
Partner: UNT Libraries Government Documents Department

Capella Corona Revisited: a Combined View from Textit XMM-Newton RGS, Textit Chandra HETGS, and LETGS

Description: We present a combined analysis of the X-ray emission of the Capella corona obtained with XMM-Newton RGS, Chandra HETGS, and LETGS. An improved atomic line database and a new differential emission measure (DEM) deconvolution method are developed for this purpose. Our new atomic database is based on the Astrophysical Plasma Emission Database and incorporates improved calculations of ionization equilibrium and line emissivities for L-shell ions of abundant elements using the Flexible Atomic Code. The new DEM deconvolution method uses a Markov Chain Monte-Carlo (MCMC) technique which differs from existing MCMC or {chi}{sup 2}-fitting based methods. We analyze the advantages and disadvantages of each individual instrument in determining the DEM and elemental abundances. We conclude that results from either RGS or HETGS data alone are not robust enough due to their failure to constrain DEM in some temperature region or the lack of significant continuum emission in the wavelength band of the spectrometers, and that the combination of HETGS and RGS gives more stringent constraints on the DEM and abundance determinations. Using the LETGS data, we show that the recently discovered inconsistencies between the EUV and X-ray lines of Fe XVIII and XIX also exist in more highly charged iron ions, up to Fe XXIII, and that enhanced interstellar absorption due to partially ionized plasma along the Capella line of sight may explain some, but not all, of these discrepancies.
Date: June 19, 2006
Creator: Gu, Ming Feng; Gupta, R.; Peterson, J.R.; Sako, M.; Kahn, S.M. & /Stanford U., Phys. Dept. /KIPAC, Menlo Park
Partner: UNT Libraries Government Documents Department

Enhancing Scalability of Sparse Direct Methods

Description: TOPS is providing high-performance, scalable sparse direct solvers, which have had significant impacts on the SciDAC applications, including fusion simulation (CEMM), accelerator modeling (COMPASS), as well as many other mission-critical applications in DOE and elsewhere. Our recent developments have been focusing on new techniques to overcome scalability bottleneck of direct methods, in both time and memory. These include parallelizing symbolic analysis phase and developing linear-complexity sparse factorization methods. The new techniques will make sparse direct methods more widely usable in large 3D simulations on highly-parallel petascale computers.
Date: July 23, 2007
Creator: Li, Xiaoye S.; Demmel, James; Grigori, Laura; Gu, Ming; Xia,Jianlin; Jardin, Steve et al.
Partner: UNT Libraries Government Documents Department