Parameter estimation for nonincreasing exponential sums by Prony-like methods

Potts, Daniel; Tasche, Manfred

doi:10.1016/j.laa.2012.10.036

Cited by 112 publications

(124 citation statements)

References 26 publications

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“…Such an approximation can be obtained with the help of the well-known ESPRIT algorithm [45], see Potts and Tasche [46] for instance, or by using the Remez algorithm, which has been applied by Hackbusch [47]. …”

Section: Efficient Computation Of the Resulting Rms Errorsmentioning

confidence: 99%

Parameter Tuning for the NFFT Based Fast Ewald Summation

Nestler

2016

Front. Phys.

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The computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditions is possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT). In this paper we consider the particle-particle NFFT (P 2 NFFT) approach, which is based on the fast Fourier transform for nonequispaced data (NFFT) and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. Typically B-splines are applied in the scope of particle mesh methods, as for instance within the well-known particle-particle particle-mesh (P 3 M) algorithm. The publicly available P 2 NFFT algorithm allows the application of an oversampled FFT as well as the usage of different window functions. We consider for the first time also an approximation by Bessel functions and show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that, if the parameters are tuned appropriately, the Bessel window function is in many cases even the better choice in terms of computational costs. Moreover, the results indicate that it is often advantageous in terms of efficiency to spend some oversampling within the NFFT while using a window function with a smaller support.

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Section: Efficient Computation Of the Resulting Rms Errorsmentioning

confidence: 99%

Parameter Tuning for the NFFT Based Fast Ewald Summation

Nestler

2016

Front. Phys.

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“…Further approaches to methods for parameter identification include MUSIC [49], ESPRIT [48] or the matrix pencil method [24]. Some of these methods have shown to be Prony-like by Potts and Tasche in [46]. Moreover, it has been shown in [37] that Prony's method is equivalent to the annihilating filter method, see e.g.…”

Section: Solve the Hankel Systemmentioning

confidence: 99%

Deterministic sparse FFT algorithms

Wannenwetsch

2015

Proc Appl Math and Mech

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In this paper we consider sparse signals ${\bf x}\in {\bf C}^N$ which are known to vanish outside a support interval of length bounded by m < N. For the case that m is known, we propose a deterministic algorithm of complexity ${\cal O}(m\log m)$ for reconstruction of x from its discrete Fourier transform $\widehat{\bf x}\in {\bf C}^N.$ (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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“…Recently, G. Plonka and T. Peter [23] generalized the Prony method to reconstruct M -sparse expansions of generalized eigenfunctions of a linear operator from O(M ) suitable values in a deterministic way. This method includes the parameter identification problem [27,3,25], the multivariate polynomial interpolation problem [2], and sparse polynomial interpolation problems in various polynomial bases [7,26]. The main drawback of the Prony method is that it may be unstable in some cases.…”

Section: Introductionmentioning

confidence: 99%

“…A simple but powerful method is to use more sampled values in combination with stable numerical methods. From the numerical point of view, this problem can be solved by the matrix pencil method [17,9,25]. However the main disadvantage is the high computational cost of the matrix pencil method.…”

Section: Introductionmentioning

confidence: 99%