Computation of adaptive Fourier series by sparse approximation of exponential sums

DOI10.1007/s00041-018-9635-1zbMath1420.42002OpenAlexW2888639905WikidataQ115609275 ScholiaQ115609275MaRDI QIDQ2003603

Vlada Pototskaia, Gerlind Plonka-Hoch

Publication date: 9 July 2019

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-018-9635-1

zbMATH Keywords

convergence rateTakenaka-Malmquist basisinfinite Hankel matricesAAK theoryadaptive Fourier seriesadaptive Fourier sumprony method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Approximation by other special function classes (41A30)

Related Items (9)

Exact reconstruction of extended exponential sums using rational approximation of their Fourier coefficients ⋮ Pole recovery from noisy data on imaginary axis ⋮ ESPRIT versus ESPIRA for reconstruction of short cosine sums and its application ⋮ The generalized operator based Prony method ⋮ Optimal rank-1 Hankel approximation of matrices: Frobenius norm and spectral norm and Cadzow's algorithm ⋮ Optimal approximation with exponential sums by a maximum likelihood modification of Prony's method ⋮ Multi-kernel unmixing and super-resolution using the modified matrix pencil method ⋮ Modifications of Prony's method for the recovery and sparse approximation with generalized exponential sums ⋮ Exact reconstruction of sparse non-harmonic signals from their Fourier coefficients

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Parameter estimation for nonincreasing exponential sums by Prony-like methods
• Sparse approximation of functions using sums of exponentials and AAK theory
• On bounded bilinear forms
• Sharp estimates for singular values of Hankel operators
• Signal processing. Part II: Control theory and applications. Based on lectures held at the IMA, Minneapolis, MN (USA) from June 27 to August 5, 1988
• Discrete \(H^\infty\)-optimization. With applications in signal processing and control systems.
• Adaptive Fourier series---a variation of greedy algorithm
• On approximation of functions by exponential sums
• On two problems concerning linear transformations in Hilbert space
• On Completely Continuous Hankel Matrices
• An Introduction to Operators on the Hardy-Hilbert Space
• Asymptotic Behavior of Eigenvalues of Hankel Operators
• Algebraic and Spectral Properties of General Toeplitz Matrices
• The fundamental role of general orthonormal bases in system identification
• Algorithm of Adaptive Fourier Decomposition
• On the Singular Values of Matrices with Displacement Structure
• Fast and Accurate Con-Eigenvalue Algorithm for Optimal Rational Approximations
• Accurate Singular Value Decompositions of Structured Matrices
• Prony methods for recovery of structured functions
• Hankel Matrices
• ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEM

This page was built for publication: Computation of adaptive Fourier series by sparse approximation of exponential sums