Browsing by Author "Yang, C."

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    A Truncated RQ-iteration for Large Scale Eigenvalue Calculations
    (1996-04) Sorensen, D.C.; Yang, C.
    We introduce a new Krylov subspace iteration for large scale eigenvalue problems that is able to accelerate the convergence through an inexact (iterative) solution to a shift-invert equation. The new method can take also full advantage of an exact solution when it is possible to apply a sparse direct method to solve the shift-invert equations. We call this new iteration the Truncated RQ Iteration (TRQ). It is based upon a recursion that develops in the leading kcolumns of the implicitly shifted RQ-Iteration for dense matrices. The main advantage in the large scale setting is that inverse-iteration like convergence occurs in the leading column of the updated basis vectors. The leading k-terms of a Schur decomposition rapidly emerge with desired eigenvalues appearing on the leading diagonal elements of the triangular matrix of the Schur decomposition. The updating equations for TRQ have a great deal in common with the update equations that define the Rational Krylov Method of Ruhe, and also the projected correction equations that define the Jacobi-Davidson Method of Van der Vorst et. al. The TRQ Iteration is quite competitive with the Rational Krylov Method when the shift-invert equations can be solved directly and with the Jacobi-Davidson Method when these equations are solved inexactly with a preconditioned iterative method. The TRQ Iteration is derived directly from the RQ-Iteration and thus inherits the convergence properties of that method. Existing RQ deflation strategies may be employed when necessary.
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    Accelerating the Lanczos Algorithm via Polynomial Spectral Transformations
    (1997-11) Sorensen, D.C.; Yang, C.
    We consider the problem of computing a few clustered and/or interior eigenvalues of a symmetric matrix A without using a matrix factorization. This can be done by applying the Lanczos algorithm to p(A), where p(lambda) is a polynomial that maps the clustered and/or interior eigenvalues of A to extremal and well separated eigenvalues of p(A). We will demonstrate and compare several techniques of constructing these polynomials. Numerical examples are presented to illustrate the effectiveness of using these polynomial to accelerate the Lanczos process.
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    An Efficient Algorithm for Calculating the Heat Capacity of a Large-scale Molecular System
    (2001-02) Yang, C.; Noid, D.W.; Sumpter, B.G.; Sorensen, D.C.; Tuzun, R.E.
    We present an efficient algorithm for computing the heat capacity of a large-scale molecular system. The new algorithm is based on a special Gaussian quadrature whose abscissas and weights are obtained by a simple Lanczos iteration. Our numerical results have indicated that this new computational scheme is quite accurate. We have also shown that this method is at least a hundred times faster than the earlier apporach that is based on esitimating the density of states and integrating with a simple quadrature formula.
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    Fermi-LAT Observations of LIGO/Virgo Event GW170817
    (IOP Publishing, 2018) Ajello, M.; Allafort, A.; Axelsson, M.; Baldini, L.; Barbiellini, G.; Baring, M.G.; Bastieri, D.; Bellazzini, R.; Berenji, B.; Bissaldi, E.; Blandford, R.D.; Bloom, E.D.; Bonino, R.; Bottacini, E.; Brandt, T.J.; Bregeon, J.; Bruel, P.; Buehler, R.; Burnett, T.H.; Buson, S.; Cameron, R.A.; Caputo, R.; Caraveo, P.A.; Casandjian, J.M.; Cavazzuti, E.; Chekhtman, A.; Cheung, C.C.; Chiang, J.; Chiaro, G.; Ciprini, S.; Cohen-Tanugi, J.; Cominsky, L.R.; Costantin, D.; Cuoco, A.; Cutini, S.; D’Ammando, F.; de Palma, F.; Di Lalla, N.; Di Mauro, M.; Di Venere, L.; Dubois, R.; Dumora, D.; Favuzzi, C.; Ferrara, E.C.; Franckowiak, A.; Fukazawa, Y.; Funk, S.; Fusco, P.; Gargano, F.; Gasparrini, D.; Giglietto, N.; Gill, R.; Giordano, F.; Giroletti, M.; Glanzman, T.; Granot, J.; Green, D.; Grenier, I.A.; Grondin, M.-H.; Guillemot, L.; Guiriec, S.; Harding, A.K.; Hays, E.; Horan, D.; Imazato, F.; Jóhannesson, G.; Kamae, T.; Kensei, S.; Kocevski, D.; Kuss, M.; La Mura, G.; Larsson, S.; Latronico, L.; Li, J.; Longo, F.; Loparco, F.; Lovellette, M.N.; Lubrano, P.; Magill, J.D.; Maldera, S.; Manfreda, A.; Mazziotta, M.N.; Michelson, P.F.; Mizuno, T.; Moiseev, A.A.; Monzani, M.E.; Moretti, E.; Morselli, A.; Moskalenko, I.V.; Negro, M.; Nuss, E.; Ojha, R.; Omodei, N.; Orlando, E.; Ormes, J.F.; Palatiello, M.; Paliya, V.S.; Paneque, D.; Persic, M.; Pesce-Rollins, M.; Petrosian, V.; Piron, F.; Porter, T.A.; Principe, G.; Racusin, J.L.; Rainò, S.; Rando, R.; Razzano, M.; Razzaque, S.; Reimer, A.; Reimer, O.; Ritz, S.; Rochester, L.S.; Ryde, F.; Parkinson, P.M. Saz; Sgrò, C.; Siskind, E.J.; Spada, F.; Spandre, G.; Spinelli, P.; Suson, D.J.; Tajima, H.; Takahashi, M.; Tak, D.; Thayer, J.G.; Thayer, J.B.; Torres, D.F.; Torresi, E.; Tosti, G.; Troja, E.; Valverde, J.; Venters, T.M.; Vianello, G.; Wood, K.; Yang, C.; Zaharijas, G.
    We present the Fermi Large Area Telescope (LAT) observations of the binary neutron star merger event GW170817 and the associated short gamma-ray burst (SGRB) GRB 170817A detected by the Fermi Gamma-ray Burst Monitor. The LAT was entering the South Atlantic Anomaly at the time of the LIGO/Virgo trigger (t GW) and therefore cannot place constraints on the existence of high-energy (E > 100 MeV) emission associated with the moment of binary coalescence. We focus instead on constraining high-energy emission on longer timescales. No candidate electromagnetic counterpart was detected by the LAT on timescales of minutes, hours, or days after the LIGO/Virgo detection. The resulting flux upper bound (at 95% C.L.) from the LAT is 4.5 × 10−10 erg cm−2 s−1 in the 0.1–1 GeV range covering a period from t GW + 1153 s to t GW + 2027 s. At the distance of GRB 170817A, this flux upper bound corresponds to a luminosity upper bound of 9.7 × 1043 erg s−1, which is five orders of magnitude less luminous than the only other LAT SGRB with known redshift, GRB 090510. We also discuss the prospects for LAT detection of electromagnetic counterparts to future gravitational-wave events from Advanced LIGO/Virgo in the context of GW170817/GRB 170817A.