The Toeplitz matrix T-n with generating function f(omega) = |1 - e(-i omega)|(-2d)h(omega), where d is an element of (- (1)/(2), (1)/(2)) \ {0} and h(omega) is positive, continuous on [- pi, pi], and differentiable on...
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The Toeplitz matrix T-n with generating function f(omega) = |1 - e(-i omega)|(-2d)h(omega), where d is an element of (- (1)/(2), (1)/(2)) \ conjugate and h(omega) is positive, continuous on [- pi, pi], and differentiable on [-pi, pi] \ conjugate, has a Fisher - Hartwig singularity [ M. E. Fisher and R. E. Hartwig (1968), Adv. Chem. Phys., 32, pp. 190 - 225]. The complexity of the preconditioned conjugategradient (PCG) algorithm is known [R. H. Chan and M. Ng (1996), SIAM Rev., 38, pp. 427 - 482] to be O(nlogn) for Toeplitz systems when d = 0. However, the effect on the PCG algorithm of the Fisher - Hartwig singularity in Tn has not been explored in the literature. We show that the complexity of the conjugategradient (CG) algorithm for solving T(n)x = b without any preconditioning grows asymptotically as n(1+|d|) log(n). With T. Chan's optimal circulant preconditioner C-n [T. Chan (1988), SIAM J. Sci. Statist. Comput., 9, pp. 766 - 771], the complexity of the PCG algorithm is O(nlog(3)(n)).
Quaternions are a tool used to describe motions of rigid bodies in R-3, (Kuipers, [15]). An interesting application is the topic of moving surfaces (Traversoni, [21]), where quaternion interpolation is used which requ...
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Quaternions are a tool used to describe motions of rigid bodies in R-3, (Kuipers, [15]). An interesting application is the topic of moving surfaces (Traversoni, [21]), where quaternion interpolation is used which requires solving equations with quaternion coefficients. In this paper we investigate the well known conjugate gradient algorithm (cg-algorithm) introduced by Hestenes and Stiefel [10] applied to quaternion valued, hermitean, positive definite matrices. We shall show, that the features known from the real case are still valid in the quaternion case. These features are: error propagation, early stopping, cg-algorithm as iterative process with error estimates, applicability to indefinite matrices. We have to present some basic facts about quaternions and about matrices with quaternion entries, in particular, about eigenvalues of such matrices. We also present some numerical examples of quaternion systems solved by the cg-algorithm.
The performance of adaptive beamforming techniques is limited by the nonhomogeneous clutter scenario. An augmented Krylov subspace method is proposed, which utilizes only a single snapshot of the data for adaptive pro...
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The performance of adaptive beamforming techniques is limited by the nonhomogeneous clutter scenario. An augmented Krylov subspace method is proposed, which utilizes only a single snapshot of the data for adaptive processing. The novel algorithm puts together a data preprocessor and adaptive Krylov subspace algorithm, where the data preprocessor suppresses discrete interference and the adaptive Krylov subspace algorithm suppresses homogeneous clutter. The novel method uses a single snapshot of the data received by the array antenna to generate a cancellation matrix that does not contain the signal of interest （SOI） component, thus, it mitigates the problem of highly nonstationary clutter environment and it helps to operate in real-time. The benefit of not requiring the training data comes at the cost of a reduced degree of freedom （DOF） of the system. Simulation illustrates the effectiveness in clutter suppression and adaptive beamforming. The numeric results show good agreement with the proposed theorem.
Wider bandwidth allows higher data rate by transmitting narrower pulses. However, doing so would also increase the discrete channel memory length. For single-carrier communication systems this results in higher comput...
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Wider bandwidth allows higher data rate by transmitting narrower pulses. However, doing so would also increase the discrete channel memory length. For single-carrier communication systems this results in higher computational burden at the receiver. We are concerned with single-carrier nonblock transmission schemes with receiver oversampling, as they can provide higher spectral efficiency than block transmission schemes in the presence of large delay spreads. We first propose a simple finite-impulse-response (FIR) equalizer that is based on the circulant-embedding (CE) method and analyze its performance by investigating the relationship between solutions of various finite-dimensional models and the original infinite-dimensional problem. We show that under proper conditions the CE FIR equalizer converges exponentially fast to the IIR equalizer. We then focus on the conjugategradient (CG) algorithm as an efficient means for equalization that is specifically well suited for dealing with large-delay-spread channels. We discuss the importance of stopping the iterations for the CG algorithm at the right time in the presence of noise and present several reliable low-cost stopping criteria. It turns out that the CG algorithm equipped with appropriate stopping criteria can outperform MMSE equalizers. Since both the CE and the CG methods can be efficiently implemented via fast Fourier transforms, equalization complexity is only in the order of N log (N) for N data symbols. Several numerical experiments demonstrate the performance of the proposed methods.
For image deconvolution, there are more methods, such as the CLEAN algorithm, maximum entropy deconvolution and iterative reconstruction. When the image contains sharp edges, these methods are less appropriate. Recent...
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ISBN:
(纸本)9781424417339
For image deconvolution, there are more methods, such as the CLEAN algorithm, maximum entropy deconvolution and iterative reconstruction. When the image contains sharp edges, these methods are less appropriate. Recently, we attempt to improve the performance near edges. In this paper we advance a new method PRECGDT-CWT, using the standard DT-CWT(Dual Tree-Complex Wavelet Transform) filters of the (13-19) taps near orthogonal filters at level 1 together with the 14-tap Q-shift filters at levels not less than *** chose ten iterations of the PRECG(the conjugate gradient algorithm used with the Preconditioned system) search direction starting from a WaRD estimate. We also compare the results with alternative deconvolution algorithms. The method of PRECGDT-CWT performs better than all the other methods tested and the published results on similar deconvolution experiments.
A flow search approach is presented in this paper. In the approach, each iterative process involves a subproblem, whose variables are the stepsize parameters. Every feasible solution of the subproblem corresponds to s...
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A flow search approach is presented in this paper. In the approach, each iterative process involves a subproblem, whose variables are the stepsize parameters. Every feasible solution of the subproblem corresponds to some serial search stages, the stepsize parameters in different search stages may interact mutually, and their optimal values are determined by evaluating the total effect of the interaction. The main idea of the flow search approach is illustrated via the minimization of a convex quadratic function. Based on the flow search approach, some properties of the m-step linear conjugate gradient algorithm are analyzed and new bounds on its convergence rate are also presented. Theoretical and numerical results indicate that the new bounds are better than the well-known ones.
One of the most powerful iterative schemes for solving symmetric, positive definite linear systems is the conjugate gradient algorithm of Hestenes and Stiefel [J. Res. Nat. Bur. Standards, 49 ( 1952), pp. 409-435], es...
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One of the most powerful iterative schemes for solving symmetric, positive definite linear systems is the conjugate gradient algorithm of Hestenes and Stiefel [J. Res. Nat. Bur. Standards, 49 ( 1952), pp. 409-435], especially when it is combined with preconditioning (cf. [ P. Concus, G. H. Golub, and D. P. O'Leary, in Proceedings of the Symposium on Sparse Matrix Computations, Argonne National Laboratory, 1975, Academic, New York, 1976]). In many applications, the solution of a sequence of equations with the same coefficient matrix is required. We propose an approach based on a combination of the conjugategradient method with Chebyshev filtering polynomials, applied only to a part of the spectrum of the coefficient matrix, as preconditioners that target some specific convergence properties of the conjugategradient method. We show that our preconditioner puts a large number of eigenvalues near one and do not degrade the distribution of the smallest ones. This procedure enables us to construct a lower dimensional Krylov basis that is very rich with respect to the smallest eigenvalues and associated eigenvectors. A major benefit of our method is that this information can then be exploited in a straightforward way to solve sequences of systems with little extra work. We illustrate the performance of our method through numerical experiments on a set of linear systems.
The performance of adaptive beamforming techniques is limited by the nonhomogeneous clutter scenario. An augmented Krylov subspace method is proposed, which utilizes only a single snapshot of the data for adaptive pro...
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The performance of adaptive beamforming techniques is limited by the nonhomogeneous clutter scenario. An augmented Krylov subspace method is proposed, which utilizes only a single snapshot of the data for adaptive processing. The novel algorithm puts together a data preprocessor and adaptive Krylov subspace algorithm, where the data preprocessor suppresses discrete interference and the adaptive Krylov subspace algorithm suppresses homogeneous clutter. The novel method uses a single snapshot of the data received by the array antenna to generate a cancellation matrix that does not contain the signal of interest (SOI) component, thus, it mitigates the problem of highly nonstationary clutter environment and it helps to operate in real-time. The benefit of not requiring the training data comes at the cost of a reduced degree of freedom (DOF) of the system. Simulation illustrates the effectiveness in clutter suppression and adaptive beamforming. The numeric results show good agreement with the proposed theorem.
作者：
葛洪海许金余School of Mechanics
Civil Engineering and Architecture Northwestern Polytechnical University
An analytical solution for the natural frequencies of a beam containing a cavity on an elastic foundation is presented. Based on the analytical solution, a numerical method for identifying cavities in the foundation i...
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An analytical solution for the natural frequencies of a beam containing a cavity on an elastic foundation is presented. Based on the analytical solution, a numerical method for identifying cavities in the foundation is developed. The position and size of the cavities are identified by minimizing an objective function, which is formulated according to the difference between the computed and measured natural frequencies of the system. The conjugate gradient algorithm is adopted for minimizing the objective function. Some numerical examples are presented to demonstrate the applicability of the presented cavity determination method. The results show that the presented method can be used to identify the cavity position and size conveniently and efficiently.
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