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A renormalization scheme for calculating the spectrum of a vibronic system occurring in molecules or impurities in insulators

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PHYSICA B-CONDENSED MATTER 2008年第18期403卷 3093-3096页

作者： Baher, S. Mehrjoo, S. Lorestan Univ Dept Phys Khorramabad *** Iran

An iteration scheme which makes use of a numerical renormalization group approach is used to calculate the spectrum of vibronic levels. This spectrum resulted from dynamic effects occurring in certain molecules or impurities in insulators. The Hamiltonian of these systems is expressed in the matrix form, using products of suitable electron-phonon states as a basis. In applying this method to multimode electron-phonon systems, phonon modes are coupled in a chain-like fashion. Then a finite chain calculation in terms of Hubbard X-operators is explored by setting up the vibronic Hamiltonian. Calculations are based on lanczos algorithm, in which only the nearest neighbor matrix elements along the chain need to be taken into account. The iterative scheme is then applied to a two-level electronic system coupled to phonons. A single-particle Green's function corresponding to a two-level system is applied to calculate the spectral density of states, which, coupled to single mode is carried out. The strength of lines in density of states is affected by the coupling constant as well as the temperature dependence of some measurable quantities. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Hubbard X-operators Green's function density of states lanczos algorithm two-level system

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FAST SUBSPACE-BASED SYSTEM-IDENTIFICATION - AN INSTRUMENTAL VARIABLE APPROACH

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AUTOMATICA 1995年第6期31卷 903-905页

作者： CHO, YM KAILATH, T Information Systems Laboratory Stanford University Stanford CA 94305-4055 U.S.A.

Recently developed subspace-based system identification (4SID) techniques have opened new routes to the identification of multi-input multi-output systems. The 4SID techniques guarantee convergence, and run faster than the statistically efficient prediction error methods without much performance loss. The resulting computational load of the 4SID techniques is O(NM(2)), where N is the data length and M is the sliding window size. However, the computational burden O(NM(2)) can become prohibitively large as N and M grow large. Noting that the major bottleneck comes from the QR factorization of an M X N data matrix and that the existing 4SID techniques do not exploit the structure of the matrices arising in the identification procedure, we propose a new implementation of the existing 4SID, which reduces the computational burden to O(NM) by exploiting the displacement and low-rank structure of the matrices.

关键词： SUBSPACE SYSTEM IDENTIFICATION INSTRUMENTAL VARIABLE DISPLACEMENT STRUCTURE SCHUR algorithm lanczos algorithm

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Quantum search in structured database using local adiabatic evolution and spectral methods

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QUANTUM INFORMATION PROCESSING 2013年第8期12卷 2813-2831页

作者： Sufiani, R. Bahari, N. Univ Tabriz Dept Theoret Phys & Astrophys Tabriz 51664 Iran Inst Studies Theoret Phys & Math Tehran 193951795 Iran

Since Grover's seminal work which provides a way to speed up combinatorial search, quantum search has been studied in great detail. We propose a new method for designing quantum search algorithms for finding a marked element in the state space of a graph. The algorithm is based on a local adiabatic evolution of the Hamiltonian associated with the graph. The main new idea is to apply some techniques such as Krylov subspace projection methods, lanczos algorithm and spectral distribution methods. Indeed, using these techniques together with the second-order perturbation theory, we give a systematic method for calculating the approximate search time at which the marked state can be reached. That is, for any undirected regular connected graph which is considered as the state space of the database, the introduced algorithm provides a systematic and programmable way for evaluation of the search time, in terms of the corresponding graph polynomials.

关键词： Quantum search algorithm Local adiabatic evolution Graph Krylov subspace lanczos algorithm Spectral distribution Second-order perturbation theory

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Fitting large-scale structured additive regression models using Krylov subspace methods

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2017年第0期105卷 59-75页

作者： Schmidt, Paul Muehlau, Mark Schmid, Volker Univ Munich Dept Stat Munich Germany Tech Univ Munich Dept Neurol Munich Germany Tech Univ Munich TUM Neuroimaging Ctr Munich Germany

Fitting regression models can be challenging when regression coefficients are high dimensional. Especially when large spatial or temporal effects need to be taken into account the limits of computational capacities of normal working stations are reached quickly. The analysis of images with several million pixels, where each pixel value can be seen as an observation on a new spatial location, represent such a situation. A Markov chain Monte Carlo (MCMC) framework for the applied statistician is presented that allows to fit models with millions of parameters with only low to moderate computational requirements. The method combines a modified sampling scheme with novel accomplishments in iterative methods for sparse linear systems. This way a solution is given that eliminates potential computational burdens such as calculating the log-determinant of massive precision matrices and sampling from high-dimensional Gaussian distributions. In an extensive simulation study with models of moderate size it is shown that this approach gives results that are in perfect agreement with state-of-the-art methods for fitting structured additive regression models. Furthermore, the method is applied to two real world examples from the field of medical imaging. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Markov chain Monte Carlo Krylov subspace methods lanczos algorithm Structured additive regression Gaussian Markov random field Image analysis

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The vibration-rotation-tunneling spectrum of the polar and T-shaped-N-in isomers of (NNO)₂

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JOURNAL OF MOLECULAR SPECTROSCOPY 2011年第1-2期268卷 53-65页

作者： Wang, Xiao-Gang Carrington, Tucker, Jr. Dawes, Richard Jasper, Ahren W. Queens Univ Dept Chem Kingston ON K7L 3N6 Canada Missouri Univ Sci & Technol Rolla MO 65401 USA Sandia Natl Labs Combust Res Facil Livermore CA 94551 USA

In this paper we report transition frequencies and line strengths computed for bright states of the NNO dimer. We use a previously reported potential obtained from explicitly correlated coupled-cluster calculations and fit using an interpolating moving least-squares method. The rovibrational Schroedinger equation is solved with a symmetry adapted lanczos algorithm and an uncoupled product basis set. All four inter-molecular coordinates are included in the calculation. We propose two tools for associating rovibrational wavefunctions with vibrational states and use them to find polar-like and T-shaped-N-in-like rovibrational states. The first tool uses a re-expansion of the rovibrational wavefunction in terms of J = 0 eigenfunctions. The second uses intensities. Calculated rotational transition frequencies are in very close agreement with experiment. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Van der Waals molecules Rovibrational spectroscopy lanczos algorithm Rovibrational intensities

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A simple analytical parameterization for the water vapor millimeter wave foreign continuum

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JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER 2003年第1-4期82卷 517-531页

作者： Ma, Q Tipping, RH Columbia Univ Dept Appl Phys NASA Goddard Inst Space Studies New York NY 10025 USA Univ Alabama Dept Phys & Astron Tuscaloosa AL 35487 USA

We present a theoretical calculation of the millimeter wave foreign continuum due to colliding pairs of H2O-N-2 molecules. The theory is formulated using the symmetrized spectral density which ensures that the principle of detailed balance is. satisfied. It is based on the lanczos algorithm, and the resulting tri-diagonal matrix is written in terms of continued fractions. The calculations are carried out in the coordinate representation in which the basis functions are delta functions whose arguments are the angular variables necessary to specify the molecular orientations. In this representation, the anisotropic interaction potential responsible for the continuum absorption is diagonal, and the ensemble averages over the states become. multidimensional integrations. These are computed using the Monte Carlo method. The results, computed for a range of temperatures relevant to the atmosphere, are compared to laboratory measurements and to widely used empirical models. For easy use, we fit our results for the absorption coefficient to a simple analytic function of frequency and temperature. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： millimeter wave absorption water vapor lanczos algorithm

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An Ab Initio Potential Energy Surface and Vibrational Energy Levels of ZnH₂

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JOURNAL OF COMPUTATIONAL CHEMISTRY 2010年第5期31卷 986-993页

作者： Huang, Zheng Guo Yu, Lei Dai, Yu Mei Tianjin Normal Univ Chem & Life Sci Coll Tianjin Key Lab Struct & Performance Funct Mol Tianjin 300387 Peoples R China

A three-dimensional potential energy surface of the electronic (,round state of ZnH2 (X-1 Sigma(+)(g)) molecule is constructed front more than 7500 ab initio points calculated at the internally contracted multireference, configuration interaction with the Davidson correction (icMRCI+Q) level employing large basis sets. The calculated relative energies of various dissociation reactions are in good agreement with the previous theoretical/experimental values. Low-lying vibrational energy levels of ZnH2, ZnD2, and HZnD are calculated on the three-dimensional potential energy surface Using the lanczos algorithm, and found to be in good agreement with the available experimental hand origins and the previous theoretical Values. (C) 2009 Wiley Periodicals. Inc. J Comput Chem 31: 986-993 2010

关键词： potential energy surface vibrational energy levels ZnH2 icMRCI lanczos algorithm

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Efficient on-the-fly interpolation technique for Bethe-Salpeter calculations of optical spectra

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COMPUTER PHYSICS COMMUNICATIONS 2016年 203卷 83-93页

作者： Gillet, Yannick Giantomassi, Matteo Gonze, Xavier Catholic Univ Louvain Inst Condensed Matter & Nanosci European Theoret Spect Facil Chemin Etoiles 8Bte L7-03-01 B-1348 Louvain La Neuve Belgium

The Bethe-Salpeter formalism represents the most accurate method available nowadays for computing neutral excitation energies and optical spectra of crystalline systems from first principles. Bethe-Salpeter calculations yield very good agreement with experiment but are notoriously difficult to converge with respect to the sampling of the electronic wavevectors. Well-converged spectra therefore require significant computational and memory resources, even by today's standards. These bottlenecks hinder the investigation of systems of great technological interest. They are also barriers to the study of derived quantities like piezoreflectance, thermoreflectance or resonant Raman intensities. We present a new methodology that decreases the workload needed to reach a given accuracy. It is based on a doublepgrid on-the-fly interpolation within the Brillouin zone, combined with the lanczos algorithm. It achieves significant speed-up and reduction of memory requirements. The technique is benchmarked in terms of accuracy on silicon, gallium arsenide and lithium fluoride. The scaling of the performance of the method as a function of the Brillouin Zone point density is much better than a conventional implementation. We also compare our method with other similar techniques proposed in the literature. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Bethe-Salpeter Equation lanczos algorithm

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Model Order Reduction for Linear Time-Invariant System With Symmetric Positive-Definite Matrices: Synthesis of Cauer-Equivalent Circuit

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IEEE TRANSACTIONS ON MAGNETICS 2020年第3期56卷 1-8页

作者： Hiruma, Shingo Igarashi, Hajime Hokkaido Univ Grad Sch Informat Sci & Technol Sapporo Hokkaido 0600814 Japan JSPS Tokyo 1020083 Japan

This article introduces a new model order reduction method for a linear time-invariant system with symmetric positive-definite matrices. The proposed method allows the construction of a reduced model, represented by a Cauer-equivalent circuit, from the original system. The method is developed by extending the Cauer ladder network method for the quasi-static Maxwell's equations, which is shown to be regarded as the lanczos algorithm with respect to a self-adjoint matrix. As a numerical example, a Cauer-equivalent circuit is generated from a simple mathematical model as well as the finite-element (FE) model of a magnetic reactor that is driven by a pulsewidth modulation voltage wave. The instantaneous power obtained from the circuit analysis is shown to be in good agreement with that obtained from the original FE model.

关键词： Continued fraction Krylov subspace methods lanczos algorithm Pade approximation self adjoint matrix transfer function

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Accelerating and parallelizing minimizations in ensemble and deterministic variational assimilations

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QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY 2012年第667期138卷 1599-1610页

作者： Desroziers, Gerald Berre, Loik Meteo France CNRS CNRM GAME F-31057 Toulouse France

The specification of a correct background-error covariance matrix is a key issue in data assimilation schemes. The Ensemble Kalman Filter (EnKF) aims at providing simulations of analysis and background errors and then gives a way to determine this background-error covariance matrix. The EnKF can be transposed to variational ensemble assimilation, where a set of perturbed variational analyses are performed. In this case, however, there is an evident important additional cost associated with the use of multiple minimizations. The aim of the paper is to investigate different techniques to reduce the cost of the multiple minimizations that have to be performed. In particular, the use is investigated of a preconditioning technique based on Ritz eigenpairs resulting from a first minimization performed by a combined lanczos/conjugate-gradient algorithm. The possibility is also studied of improving the starting point of a new perturbed solution, with lanczos vectors issued from a single prior unperturbed or perturbed minimization. This appears to provide a first significant reduction in the cost of the new minimization. Finally, a new approach is proposed to generalize the previous idea to the use of multiple sets of lanczos vectors issued from an ensemble of perturbed assimilations. The application of this procedure to a simplified analysis problem shows encouraging results, as it appears to be a possible way for reducing the global cost of an ensemble variational assimilation. Moreover, this seems to provide an efficient strategy for parallelizing such an ensemble variational assimilation but also the deterministic variational assimilation itself. Copyright (c) 2012 Royal Meteorological Society

关键词： lanczos algorithm conjugate-gradient algorithm

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