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Application of the AAK theory and Prony‐like Methods for sparse approximation of exponential sums
Author(s) -
Pototskaia Vlada,
Plonka Gerlind
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710385
Subject(s) - exponential function , exponential sum , mathematics , norm (philosophy) , exponential formula , algorithm , double exponential function , mathematical analysis , political science , law
Abstract We derive a new method for optimal ℓ 2 ‐approximation of discrete signals on ℓ 2 (ℕ 0 ) whose entries can be represented as an exponential sum of finite length. Our approach employs Prony's method in a first step to recover the exponential sum that is determined by the signal. In the second step we use the theory of Adamjan, Arov and Krein (AAK) to derive an algorithm for computing a shorter exponential sum that approximates the original signal in the ℓ 2 ‐norm well. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)