Prony methods for recovery of structured functions
Prony methods for recovery of structured functions
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DOI：
10.1002/gamm.201410011
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发表时间：
2014-11
期刊：
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通讯作者：
G. Plonka;M. Tasche
中科院分区：
文献类型：
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作者：
G. Plonka;M. Tasche
本文介绍了经典的proony方法及其同类方法。我们概述了一种常用的类似于prony的方法来处理等距采样数据，即ESPRIT方法。讨论了非均匀采样数据的情况。对于稀疏特征函数展开的重构，提出了一种广义proony方法。Prony方法应用于结构化函数（如指数和和和扩展指数和）和稀疏向量的恢复。从傅里叶数据中恢复具有任意结点的样条函数也是基于proony方法。最后给出了数值算例。（©2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim）
In this survey, we describe the classical Prony method and whose relatives. We sketch a frequently used Prony–like method for equispaced sampled data, namely the ESPRIT method. The case of nonequispaced sampled data is discussed too. For the reconstruction of a sparse eigenfunction expansion, a generalized Prony method is presented. The Prony methods are applied to the recovery of structured functions (such as exponential sums and extended exponential sums) and of sparse vectors. The recovery of spline functions with arbitrary knots from Fourier data is also based on Prony methods. Finally, some numerical examples are given. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)