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

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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ON EFFICIENT NUMERICAL APPROXIMATION OF THE BILINEAR FORM c* A^-1b

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2011年第2期33卷 565-587页

作者： Strakos, Zdenek Tichy, Petr Charles Univ Prague Fac Math & Phys Prague 18675 Czech Republic Acad Sci Czech Republic Inst Comp Sci Prague 18207 Czech Republic

Let A is an element of C-NxN be a nonsingular complex matrix and b and c be complex vectors of length N. The goal of this paper is to investigate approaches for efficient approximations of the bilinear form c* A(-1)b. Equivalently, we wish to approximate the scalar value c* x, where x solves the linear system Ax = b. Here the matrix A can be very large or its elements can be too costly to compute so that A is not explicitly available and it is used only in the form of the matrix-vector product. Therefore a direct method is not an option. For A Hermitian positive definite, b* A(-1)b can be efficiently approximated as a by-product of the conjugate-gradient iterations, which is mathematically equivalent to the matching moment approximations computed via the Gauss-Christoffel quadrature. In this paper we propose a new method using the biconjugate gradient iterations which is applicable to the general complex case. The proposed approach will be compared with existing ones using analytic arguments and numerical experiments.

关键词： bilinear forms scattering amplitude method of moments Krylov subspace methods conjugate gradient method biconjugate gradient method lanczos algorithm Arnoldi algorithm Gauss-Christoffel quadrature model reduction

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Theoretical study of the rovibrational spectrum of He₂-OCS

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CANADIAN JOURNAL OF CHEMISTRY-REVUE CANADIENNE DE CHIMIE 2010年第8期88卷 779-786页

作者： Wang, Xiao-Gang Carrington, Tucker, Jr. Queens Univ Dept Chem Kingston ON K7L 3N6 Canada

We report calculated microwave and infrared rovibrational transitions of the van der Waals complex He-2 - OCS. The calculations were done using a product basis, a lanczos eigensolver, and potentials built from He-OCS, and He-He potential functions taken from the literature. All five of the large amplitude coordinates are treated exactly and calculations are done for J values up to five. All rovibrational levels are converged to 0.001 cm(-1) by using basis sets with as many as 87 million funcions. Good agreement is found with previously reported experimental results. Although we assume that the dipole moment is along the OCS axis, we find transitions with appreciable intensity between different torsion states.

关键词： rovibrational spectroscopy quantum dynamics van der Waals clusters doped helium clusters 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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Quadrature rule-based bounds for functions of adjacency matrices

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LINEAR ALGEBRA AND ITS APPLICATIONS 2010年第3期433卷 637-652页

作者： Benzi, Michele Boito, Paola Emory Univ Dept Math & Comp Sci Atlanta GA 30322 USA

Bounds for entries of matrix functions based on Gauss-type quadrature rules are applied to adjacency matrices associated with graphs. This technique allows to develop inexpensive and accurate upper and lower bounds for certain quantities (Estrada index, subgraph centrality, communicability) that describe properties of networks. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Graphs Networks Estrada index Subgraph centrality Communicability Sparse matrices Quadrature rules lanczos algorithm Decay bounds Matrix exponential Resolvent

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Characterization of Sparse-Array detection Photoacoustic Tomography using the Singular Value Decomposition

Characterization of Sparse-Array detection Photoacoustic Tom...

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Conference on Photons Plus Ultrasound - Imaging and Sensing 2010

作者： Chaudhary, G. Roumeliotis, M. Ephrat, P. Stodilka, R. Carson, J. J. L. Anastasio, M. A. IIT Med Imaging Res Ctr Dept Elect & Comp Engn Chicago IL 60616 USA IIT Med Imaging Res Ctr Dept Biomed Engn Chicago IL 60616 USA St Josephs Hlth Care Lawson Hlth Res Inst Imaging Program London ON N6A 4V2 Canada Univ West Ontario Dept Med Biophys London ON N6A 5C1 Canada

ISBN: (纸本)9780819479600

A photoacoustic tomography (PAT) method that employs a sparse two-dimentional (2D) array of detector elements has recently been employed to reconstruct images of simple objects from highly incomplete measurement data. However, there remains an important need to understand what type of object features can be reliably reconstructed from such a system. In this work, we numerically compute the singular value decomposition (SVD) of different system matrices that are relevant to implementations of sparse-array PAT. For a given number and arrangement of measurement transducers, this will reveal the type of object features that can reliably be reconstructed as well as those that are invisible to the imaging system.

关键词： Photoacoustic tomography singular value decomposition lanczos algorithm pseudo-inverse solution

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Steady-state response by finite-difference time-domain method and lanczos algorithm

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2006年第7期54卷 3038-3044页

作者： Huang, Ting-Yi Wu, Ruey-Beei Natl Taiwan Univ Dept Elect Engn Taipei 106 Taiwan Natl Taiwan Univ Grad Inst Commun Engn Taipei 106 Taiwan

A hybrid method combining the finite-difference time-domain (FDTD) method and lanczos algorithm is proposed for efficiently obtaining the steady-state response for closed systems. With the lanczos algorithm, modes of the FDTD operator can be easily extracted to reconstruct the steady-state response at any time by an analytic formula. With the aid of the time-reversal technique, existing FDTD codes are preserved. Numerical results show that with only very few lanczos iterations, results of good agreement can be achieved between the proposed method and brute-force FDTD.

关键词： finite-difference time-domain (FDTD) method lanczos algorithm model-order reduction

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Fast Approximate kNN Graph Construction for High Dimensional Data via Recursive lanczos Bisection

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JOURNAL OF MACHINE LEARNING RESEARCH 2009年第9期10卷 1989-2012页

作者： Chen, Jie Fang, Haw-ren Saad, Yousef Univ Minnesota Dept Comp Sci & Engn Minneapolis MN 55455 USA Argonne Natl Lab Div Math & Comp Sci Argonne IL 60439 USA

Nearest neighbor graphs are widely used in data mining and machine learning. A brute-force method to compute the exact kNN graph takes Theta(dn(2)) time for n data points in the d dimensional Euclidean space. We propose two divide and conquer methods for computing an approximate kNN graph in Theta(dn(t)) time for high dimensional data (large d). The exponent t is an element of (1, 2) is an increasing function of an internal parameter a which governs the size of the common region in the divide step. Experiments show that a high quality graph can usually be obtained with small overlaps, that is, for small values of t. A few of the practical details of the algorithms are as follows. First, the divide step uses an inexpensive lanczos procedure to perform recursive spectral bisection. After each conquer step, an additional refinement step is performed to improve the accuracy of the graph. Finally, a hash table is used to avoid repeating distance calculations during the divide and conquer process. The combination of these techniques is shown to yield quite effective algorithms for building kNN graphs.

关键词： nearest neighbors graph high dimensional data divide and conquer lanczos algorithm spectral method

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lanczos Vectors versus Singular Vectors for Effective Dimension Reduction

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2009年第8期21卷 1091-1103页

作者： Chen, Jie Saad, Yousef Univ Minnesota Dept Comp Sci & Engn Minneapolis MN 55455 USA

This paper takes an in-depth look at a technique for computing filtered matrix-vector (mat-vec) products which are required in many data analysis applications. In these applications, the data matrix is multiplied by a vector and we wish to perform this product accurately in the space spanned by a few of the major singular vectors of the matrix. We examine the use of the lanczos algorithm for this purpose. The goal of the method is identical with that of the truncated singular value decomposition (SVD), namely to preserve the quality of the resulting mat-vec product in the major singular directions of the matrix. The lanczos-based approach achieves this goal by using a small number of lanczos vectors, but it does not explicitly compute singular values/vectors of the matrix. The main advantage of the lanczos-based technique is its low cost when compared with that of the truncated SVD. This advantage comes without sacrificing accuracy. The effectiveness of this approach is demonstrated on a few sample applications requiring dimension reduction, including information retrieval and face recognition. The proposed technique can be applied as a replacement to the truncated SVD technique whenever the problem can be formulated as a filtered mat-vec multiplication.

关键词： Dimension reduction SVD lanczos algorithm information retrieval latent semantic indexing face recognition PCA eigenfaces

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An extension of the conjugate residual method to nonsymmetric linear systems

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2009年第1期226卷 103-113页

作者： Sogabe, T. Sugihara, M. Zhang, S. -L. Nagoya Univ Dept Computat Sci & Engn Chikusa Ku Nagoya Aichi 4648603 Japan Univ Tokyo Dept Math Informat Bunkyo Ku Tokyo 1138656 Japan

The Conjugate Gradient (CG) method and the Conjugate Residual (CR) method are Krylov subspace methods for solving symmetric (positive definite) linear systems. To solve nonsymmetric linear systems, the Bi-Conjugate Gradient (Bi-CG) method has been proposed as an extension of CG. Bi-CG has attractive short-term recurrences, and it is the basis for the successful variants such as Bi-CGSTAB. In this paper, we extend CR to nonsymmetric linear systems with the aim of finding an alternative basic solver. Numerical experiments show that the resulting algorithm with short-term recurrences often gives smoother convergence behavior than Bi-CG. Hence, it may take the place of Bi-CG for the successful variants. (c) 2008 Elsevier B.V. All rights reserved.

关键词： CG CR Bi-CG Krylov subspace methods Nonsymmetric linear systems lanczos algorithm Coupled two-term recurrences

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