1,034 research outputs found
Generalized Householder Transformations for the Complex Symmetric Eigenvalue Problem
We present an intuitive and scalable algorithm for the diagonalization of
complex symmetric matrices, which arise from the projection of
pseudo--Hermitian and complex scaled Hamiltonians onto a suitable basis set of
"trial" states. The algorithm diagonalizes complex and symmetric
(non--Hermitian) matrices and is easily implemented in modern computer
languages. It is based on generalized Householder transformations and relies on
iterative similarity transformations T -> T' = Q^T T Q, where Q is a complex
and orthogonal, but not unitary, matrix, i.e, Q^T equals Q^(-1) but Q^+ is
different from Q^(-1). We present numerical reference data to support the
scalability of the algorithm. We construct the generalized Householder
transformations from the notion that the conserved scalar product of
eigenstates Psi_n and Psi_m of a pseudo-Hermitian quantum mechanical
Hamiltonian can be reformulated in terms of the generalized indefinite inner
product [integral of the product Psi_n(x,t) Psi_m(x,t) over dx], where the
integrand is locally defined, and complex conjugation is avoided. A few example
calculations are described which illustrate the physical origin of the ideas
used in the construction of the algorithm.Comment: 14 pages; RevTeX; font mismatch in Eqs. (3) and (15) is eliminate
A modal parameter extraction procedure applicable to linear time-invariant dynamic systems
Modal analysis has emerged as a valuable tool in many phases of the engineering design process. Complex vibration and acoustic problems in new designs can often be remedied through use of the method. Moreover, the technique has been used to enhance the conceptual understanding of structures by serving to verify analytical models. A new modal parameter estimation procedure is presented. The technique is applicable to linear, time-invariant systems and accommodates multiple input excitations. In order to provide a background for the derivation of the method, some modal parameter extraction procedures currently in use are described. Key features implemented in the new technique are elaborated upon
Householder QR Factorization With Randomization for Column Pivoting (HQRRP)
A fundamental problem when adding column pivoting to the Householder QR fac-
torization is that only about half of the computation can be cast in terms of high performing matrix-
matrix multiplications, which greatly limits the bene ts that can be derived from so-called blocking
of algorithms. This paper describes a technique for selecting groups of pivot vectors by means of
randomized projections. It is demonstrated that the asymptotic
op count for the proposed method
is 2mn2 �����(2=3)n3 for an m n matrix, identical to that of the best classical unblocked Householder
QR factorization algorithm (with or without pivoting). Experiments demonstrate acceleration in
speed of close to an order of magnitude relative to the geqp3 function in LAPACK, when executed
on a modern CPU with multiple cores. Further, experiments demonstrate that the quality of the
randomized pivot selection strategy is roughly the same as that of classical column pivoting. The
described algorithm is made available under Open Source license and can be used with LAPACK or
libflame
Real-time flutter identification
The techniques and a FORTRAN 77 MOdal Parameter IDentification (MOPID) computer program developed for identification of the frequencies and damping ratios of multiple flutter modes in real time are documented. Physically meaningful model parameterization was combined with state of the art recursive identification techniques and applied to the problem of real time flutter mode monitoring. The performance of the algorithm in terms of convergence speed and parameter estimation error is demonstrated for several simulated data cases, and the results of actual flight data analysis from two different vehicles are presented. It is indicated that the algorithm is capable of real time monitoring of aircraft flutter characteristics with a high degree of reliability
Efficient Synthesis of Room Acoustics via Scattering Delay Networks
An acoustic reverberator consisting of a network of delay lines connected via
scattering junctions is proposed. All parameters of the reverberator are
derived from physical properties of the enclosure it simulates. It allows for
simulation of unequal and frequency-dependent wall absorption, as well as
directional sources and microphones. The reverberator renders the first-order
reflections exactly, while making progressively coarser approximations of
higher-order reflections. The rate of energy decay is close to that obtained
with the image method (IM) and consistent with the predictions of Sabine and
Eyring equations. The time evolution of the normalized echo density, which was
previously shown to be correlated with the perceived texture of reverberation,
is also close to that of IM. However, its computational complexity is one to
two orders of magnitude lower, comparable to the computational complexity of a
feedback delay network (FDN), and its memory requirements are negligible
Model structure detection and system identification of metal rubber devices
Metal rubber (MR) devices, a new wire mesh material, have been extensively used in recent years due to several unique properties especially in adverse environments. Although many practical studies have been completed, the related theoretical research on metal rubber is still in its infancy. In this paper, a semi-constitutive dynamic model that involves nonlinear elastic stiffness, nonlinear viscous damping and bilinear hysteresis Coulomb damping is adopted to model MR devices. After approximating the bilinear hysteresis damping using Chebyshev polynomials of the first kind, a very efficient procedure based on the orthogonal least squares (OLS) algorithm and the adjustable prediction error sum of squares (APRESS) criterion is proposed for model structure detection and parameter estimation of an MR device for the first time. The OLS algorithm provides a powerful tool to effectively select the significant model terms step by step, one at a time, by orthogonalizing the associated terms and maximizing the error reduction ratio, in a forward stepwise procedure. The APRESS statistic regularizes the OLS algorithm to facilitate the determination of the optimal number of model terms that should be included into the dynamic model. Because of the orthogonal property of the OLS algorithm, the approach leads to a parsimonious model. Numerical ill-conditioning problems confronted by the conventional least squares algorithm can also be avoided by the new approach. Finally by utilising the transient response of a MR specimen, it is shown how the model structure can be detected in a practical application. The identified model agrees with the experimental measurements very well
Structural vector autoregressions: theory of identification and algorithms for inference
Structural vector autoregressions (SVARs) are widely used for policy analysis and to provide stylized facts for dynamic general equilibrium models. Yet there have been no workable rank conditions to ascertain whether an SVAR is globally identified. When identifying restrictions such as long-run restrictions are imposed on impulse responses, there have been no efficient algorithms for small-sample estimation and inference. To fill these important gaps in the literature, this paper makes four contributions. First, we establish general rank conditions for global identification of both overidentified and exactly identified models. Second, we show that these conditions can be checked as a simple matrix-filling exercise and that they apply to a wide class of identifying restrictions, including linear and certain nonlinear restrictions. Third, we establish a very simple rank condition for exactly identified models that amounts to a straightforward counting exercise. Fourth, we develop a number of efficient algorithms for small-sample estimation and inference.Vector autoregression
Privacy Preserving Distributed Data Mining
Privacy preserving distributed data mining aims to design secure protocols which allow multiple parties to conduct collaborative data mining while protecting the data privacy. My research focuses on the design and implementation of privacy preserving two-party protocols based on homomorphic encryption. I present new results in this area, including new secure protocols for basic operations and two fundamental privacy preserving data mining protocols.
I propose a number of secure protocols for basic operations in the additive secret-sharing scheme based on homomorphic encryption. I derive a basic relationship between a secret number and its shares, with which we develop efficient secure comparison and secure division with public divisor protocols. I also design a secure inverse square root protocol based on Newton\u27s iterative method and hence propose a solution for the secure square root problem. In addition, we propose a secure exponential protocol based on Taylor series expansions. All these protocols are implemented using secure multiplication and can be used to develop privacy preserving distributed data mining protocols.
In particular, I develop efficient privacy preserving protocols for two fundamental data mining tasks: multiple linear regression and EM clustering. Both protocols work for arbitrarily partitioned datasets. The two-party privacy preserving linear regression protocol is provably secure in the semi-honest model, and the EM clustering protocol discloses only the number of iterations. I provide a proof-of-concept implementation of these protocols in C++, based on the Paillier cryptosystem
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