We show in this paper how the convergence of an algorithm for matrix completion can be significantly improved by applying Wynn's e-algorithm. Straightforward generalization of the scalar e-algorithm to matrices fa...
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We show in this paper how the convergence of an algorithm for matrix completion can be significantly improved by applying Wynn's e-algorithm. Straightforward generalization of the scalar e-algorithm to matrices fails. However, accelerating the convergence of only the missing matrix elements turns out to be very successful.
An analytic examination of 3D holography under a 90 degrees recording geometry was carried out earlier in which 2D spatial Laplace transforms were introduced in order to develop transfer functions for the scattered ou...
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ISBN:
(纸本)9780819499196
An analytic examination of 3D holography under a 90 degrees recording geometry was carried out earlier in which 2D spatial Laplace transforms were introduced in order to develop transfer functions for the scattered outputs under readout [1,2]. Thereby, the resulting reconstructed output was obtained in the 2D Laplace domain whence the spatial information would be found only by performing a 2D Laplace inversion. Laplace inversion in 2D was attempted by testing a prototype function for which the analytic result was known using two known inversion algorithms, viz., the Brancik and the Abate [2]. The results indicated notable differences in the 3D plots between the algorithms and the analytic result, and hence were somewhat inconclusive. In this paper, we take a closer look at the Brancik algorithm in order to understand better the implications of the choices of key parameters such as the real and imaginary parts of the Bromwich contour and the grid sizes of the summation operations. To assess the inversion findings, three prototype test cases are considered for which the analytic solutions are known. For specific choices of the algorithm parameters, optimal values are determined that minimize errors in general. It is found that even though errors accumulate near the edges of the grid, overall reasonably accurate inversions are possible to obtain with optimal parameter choices that are verifiable via cross-sectional views. Further work is ongoing whereby the optimized algorithm is to be applied to the 3D holography problem.
In this paper, a generalized E-transformation arising from the study of a generalization of sequence transformations and triangular recursion schemes is proposed. Three new algorithms, namely, the generalized E-algori...
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In this paper, a generalized E-transformation arising from the study of a generalization of sequence transformations and triangular recursion schemes is proposed. Three new algorithms, namely, the generalized E-algorithm, the generalized FS-algorithm and the generalized hungry type E-algorithm, are constructed for implementing the generalization of the E-transformation. Some convergence results of the generalized E-algorithm are obtained. In addition, some particular cases of the generalized E-transformation and the recursive algorithms for their computation are also studied.
Using the Neumann series and epsilon-algorithm. a new dynamic response reanalysis method for modified structures under arbitrary excitation is developed. Based on the Newmark method, the approximate displacement respo...
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Using the Neumann series and epsilon-algorithm. a new dynamic response reanalysis method for modified structures under arbitrary excitation is developed. Based on the Newmark method, the approximate displacement responses in each time step can be obtained by using the epsilon-algorithm. The basis vectors obtained by the Neumann series expansion can be used to construct the vector sequences in the epsilon-algorithm table. Two numerical examples are given to demonstrate the applications of the proposed method. The comparisons of the proposed method, the full analysis of the Newmark method and the Kirsch method are given in the first numerical example. (C) 2008 Elsevier Ltd. All rights reserved.
The majority of contemporary design tools do not still contain steady-state algorithms, especially for the autonomous systems. This is mainly caused by insufficient accuracy of the algorithm for numerical integration,...
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The majority of contemporary design tools do not still contain steady-state algorithms, especially for the autonomous systems. This is mainly caused by insufficient accuracy of the algorithm for numerical integration, but also by unreliable steady-state algorithms themselves. Therefore, in the paper, a very stable and efficient procedure for the numerical integration of nonlinear differential-algebraic systems is defined first. Afterwards, two improved methods are defined for finding the steady state, which use this integration algorithm in their iteration loops. The first is based on the idea of extrapolation, and the second utilizes nonstandard time-domain sensitivity analysis. The two steady-state algorithms are compared by analyses of a rectifier and a C-class amplifier, and the extrapolation algorithm is primarily selected as a more reliable alternative. Finally, the method based on the extrapolation naturally cooperating with the algorithm for solving the differential-algebraic systems is thoroughly tested on various electronic circuits: Van der Pol and Colpitts oscillators, fragment of a large bipolar logical circuit, feedback and distributed microwave oscillators, and power amplifier. The results confirm that the extrapolation method is faster than a classical plain numerical integration, especially for larger circuits with complicated transients.
We study the epsilon-algorithm that was discussed in the papers of Guilpin et al. and Brezinski both published in 2004. Some researchers may motivate by their results to believe that is an efficient algorithm to gener...
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We study the epsilon-algorithm that was discussed in the papers of Guilpin et al. and Brezinski both published in 2004. Some researchers may motivate by their results to believe that is an efficient algorithm to generate many new series that will converge to the desired limit much faster than the original series. We will use the same example that appeared in Guilpin et al. to illustrate that some series derived by the epsilon-algorithm may not converge to the desired limit. Thus, we advise the researchers with care to look deeply into the existing literature before to use this sophisticated technique.
Based on the Neumann series expansion and epsilon-algorithm, a new eigensolution reanalysis method is developed. In the solution process, the basis vectors can be obtained using the matrix perturbation or the Neumann ...
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Based on the Neumann series expansion and epsilon-algorithm, a new eigensolution reanalysis method is developed. In the solution process, the basis vectors can be obtained using the matrix perturbation or the Neumann series expansion to construct the vector sequence, and then using the epsilonalgorithm table to obtain the approximate eigenvectors. The approximate eigenvalues are computed from the Rayleigh quotients. The solution steps are straightforward and it is easy to implement with the general finite element analysis system. Two numerical examples, a 40-storey frame and a chassis structure, are given to demonstrate the application of the present method. By comparing with the exact solutions and the Kirsch method solutions, it is shown that the excellent results are obtained for very large changes in the design, and that the accuracy of the epsilon-algorithm is higher than that of the Kirsch method and the computation time is less than that of the Kirsch method. Copyright P (c) 2005 John Wiley & Sons, Ltd.
Using interval theory and the second-order Taylor series, the eigenvalue problems of structures with multi-parameter can be transformed into those with single parameter. The epsilon-algorithm is used to accelerate the...
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Using interval theory and the second-order Taylor series, the eigenvalue problems of structures with multi-parameter can be transformed into those with single parameter. The epsilon-algorithm is used to accelerate the convergence of the Neumann series to obtain the bounds of eigenvalues of structures with single interval parameter, thus increasing the computing accuracy and reducing the computational effort. Finally, the effect of uncertain parameters on natural frequencies is evaluated. Two engineering examples show that the proposed method can give better results than those obtained by the first-order approximation, even if the uncertainties of parameters are fairly large. (C) 2009 Elsevier Ltd. All rights reserved.
Recently, Brezinski has proposed to use Wynn's epsilon-algorithm in order to reduce the Gibbs phenomenon for partial Fourier sums of smooth functions with jumps, by displaying very convincing numerical experiments...
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Recently, Brezinski has proposed to use Wynn's epsilon-algorithm in order to reduce the Gibbs phenomenon for partial Fourier sums of smooth functions with jumps, by displaying very convincing numerical experiments. In the present paper we derive analytic estimates for the error corresponding to a particular class of hypergeometric functions, and obtain the rate of column convergence for such functions, possibly perturbed by another sufficiently differentiable function. We also analyze the connection to Pade-Fourier and Pade-Chebyshev approximants, including those recently studied by Kaber and Maday. (C) 2007 Elsevier B.V. All tights reserved.
The numerical approximation of nonlinear partial differential equations requires the computation of large nonlinear systems, that are typically solved by iterative schemes. At each step of the iterative process, a lar...
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The numerical approximation of nonlinear partial differential equations requires the computation of large nonlinear systems, that are typically solved by iterative schemes. At each step of the iterative process, a large and sparse linear system has to be solved, and the amount of time elapsed per step grows with the dimensions of the problem. As a consequence, the convergence rate may become very slow, requiring massive cpu-time to compute the solution. In all such cases, it is important to improve the rate of convergence of the iterative scheme. This can be achieved, for instance, by vector extrapolation methods. In this work, we apply some vector extrapolation methods to the electronic device simulation to improve the rate of convergence of the family of Gummel decoupling algorithms. Furthermore, a different approach to the topological epsilon-algorithm is proposed and preliminary results are presented.
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