Optimal approximation with exponential sums by a maximum likelihood modification of Prony's method

DOI10.1007/s10444-019-09692-yzbMath1415.65095OpenAlexW2942469764WikidataQ115605496 ScholiaQ115605496MaRDI QIDQ2000539

Yanyan Li

Publication date: 28 June 2019

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-019-09692-y

zbMATH Keywords

nonconvex optimizationnonlinear eigenvalue problemstructured matricesProny methodnonlinear structured least squares problem

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) General nonlinear regression (62J02) Eigenvalues, singular values, and eigenvectors (15A18) Approximation by other special function classes (41A30)

Related Items (6)

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 ⋮ On algebraic properties of low rank approximations of Prony systems ⋮ 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

Uses Software

• SLRA

Cites Work

• 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
• Numerical Fourier analysis
• Low-rank approximation. Algorithms, implementation, applications
• An efficient algorithm for estimating the parameters of superimposed exponential signals
• Fixed-point algorithms for frequency estimation and structured low rank approximation
• Computation of adaptive Fourier series by sparse approximation of exponential sums
• Signal recovery by discrete approximation and a Prony-like method
• Variable projection for affinely structured low-rank approximation in weighted \(2\)-norms
• Approximation by exponential sums revisited
• Software for weighted structured low-rank approximation
• On approximation of functions by exponential sums
• An efficient algorithm for estimating the parameters of superimposed exponential signals in multiplicative and additive noise
• One Shot Inverse Scattering via Rational Approximation
• Factorization Approach to Structured Low-Rank Approximation with Applications
• Nonlinear approximation by sums of nonincreasing exponentials
• A Modified Prony Algorithm for Fitting Functions Defined by Difference Equations
• On the efficient computation of high-dimensional integrals and the approximation by exponential sums
• Some Special Nonlinear Least Squares Problems
• A Modified Prony Algorithm for Exponential Function Fitting
• Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon Meets Strang–Fix
• Reconstruction of Finite Rate of Innovation Signals with Model-Fitting Approach
• A generalized Prony method for reconstruction of sparse sums of eigenfunctions of linear operators
• Prony methods for recovery of structured functions
• ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEM
• The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate

This page was built for publication: Optimal approximation with exponential sums by a maximum likelihood modification of Prony's method