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 tha...
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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.
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 mar...
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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.
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...
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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.
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 an...
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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.
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 princip...
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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.
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 multireferen...
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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
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 calculatio...
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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.
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...
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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.
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...
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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
The weighted checksum scheme has been proposed as a low-cost fault tolerant procedure for parallel matrix computations. To guarantee multiple error detection and correction, the chosen weight vectors must satisfy some...
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The weighted checksum scheme has been proposed as a low-cost fault tolerant procedure for parallel matrix computations. To guarantee multiple error detection and correction, the chosen weight vectors must satisfy some very specific properties about linear independence. However, previous weight generating methods that fulfill the independence criteria have troubles with numerical overflow. We will present a new scheme that generates weight vectors via Chebyshev polynomials to meet the requirements about independence and to avoid the difficulties with overflow.
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