32,467 research outputs found
Parallel-vector unsymmetric Eigen-Solver on high performance computers
The popular QR algorithm for solving all eigenvalues of an unsymmetric matrix is reviewed. Among the basic components in the QR algorithm, it was concluded from this study, that the reduction of an unsymmetric matrix to a Hessenberg form (before applying the QR algorithm itself) can be done effectively by exploiting the vector speed and multiple processors offered by modern high-performance computers. Numerical examples of several test cases have indicated that the proposed parallel-vector algorithm for converting a given unsymmetric matrix to a Hessenberg form offers computational advantages over the existing algorithm. The time saving obtained by the proposed methods is increased as the problem size increased
Efficient AUC Optimization for Information Ranking Applications
Adequate evaluation of an information retrieval system to estimate future
performance is a crucial task. Area under the ROC curve (AUC) is widely used to
evaluate the generalization of a retrieval system. However, the objective
function optimized in many retrieval systems is the error rate and not the AUC
value. This paper provides an efficient and effective non-linear approach to
optimize AUC using additive regression trees, with a special emphasis on the
use of multi-class AUC (MAUC) because multiple relevance levels are widely used
in many ranking applications. Compared to a conventional linear approach, the
performance of the non-linear approach is comparable on binary-relevance
benchmark datasets and is better on multi-relevance benchmark datasets.Comment: 12 page
Impedance Analysis of Bunch Length Measurements at the ATF Damping Ring
We present energy spread and bunch length measurements at the Accelerator
Test Facility (ATF) at KEK, as functions of current, for different ring rf
voltages, and with the beam both on and off the coupling resonance. We fit the
on-coupling bunch shapes to those of an impedance model consisting of a
resistor and an inductor connected in series. We find that the fits are
reasonably good, but that the resulting impedance is unexpectedly large.Comment: 9 pages, 5 figures, presented at 10th International Symposium on
Applied Electromagnetics and Mechanics (ISEM2001
Groundstate with Zero Eigenvalue for Generalized Sombrero-shaped Potential in -dimensional Space
Based on an iterative method for solving the goundstate of Schroedinger
equation, it is found that a kind of generalized Sombrero-shaped potentials in
N-dimensional space has groundstates with zero eigenvalue. The restrictions on
the parameters in the potential are discussed.Comment: 8 pages, 3 figure
Optimizing Hartree-Fock orbitals by the density-matrix renormalization group
We have proposed a density-matrix renormalization group (DMRG) scheme to
optimize the one-electron basis states of molecules. It improves significantly
the accuracy and efficiency of the DMRG in the study of quantum chemistry or
other many-fermion system with nonlocal interactions. For a water molecule, we
find that the ground state energy obtained by the DMRG with only 61 optimized
orbitals already reaches the accuracy of best quantum Monte Carlo calculation
with 92 orbitals.Comment: published version, 4 pages, 4 figure
Thermodynamic properties of the itinerant-boson ferromagnet
Thermodynamics of a spin-1 Bose gas with ferromagnetic interactions are
investigated via the mean-field theory. It is apparently shown in the specific
heat curve that the system undergoes two phase transitions, the ferromagnetic
transition and the Bose-Einstein condensation, with the Curie point above the
condensation temperature. Above the Curie point, the susceptibility fits the
Curie-Weiss law perfectly. At a fixed temperature, the reciprocal
susceptibility is also in a good linear relationship with the ferromagnetic
interaction.Comment: 5 pages, 5 figure
Iterative Solutions for Low Lying Excited States of a Class of Schroedinger Equation
The convergent iterative procedure for solving the groundstate Schroedinger
equation is extended to derive the excitation energy and the wave function of
the low-lying excited states. The method is applied to the one-dimensional
quartic potential problem. The results show that the iterative solution
converges rapidly when the coupling is not too small.Comment: 14 pages, 4 figure
Haldane Gap and Hidden Order in the S=2 Antiferromagnetic Quantum Spin Chain
We have investigated Haldane's conjecture for the S=2 isotropic
antiferromagnetic quantum spin chain with nearest-neighbor exchange J. Using a
density matrix renormalization group algorithm for chains up to L=350 spins, we
find in the thermodynamic limit a finite spin gap of Delta = 0.085(5)J and a
finite spin-spin correlation length xi = 49(1) lattice spacings. We establish
the ground state energy per bond to be E_0=-4.761248(1)J. We show that the
ground state has a hidden topological order that is revealed in a nonlocal
string correlation function. This means that the physics of the S=2 chain can
be captured by a valence-bond solid description. We also observe effective free
spin-1 states at the ends of an open S=2 chain.Comment: 6 pages, LaTeX 2.09, 3 PostScript figure
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