Sparse polynomial interpolation in Chebyshev bases

DOI10.1016/j.laa.2013.02.006zbMath1282.65028OpenAlexW2021099221MaRDI QIDQ2437332

Daniel Potts, Manfred Tasche

Publication date: 3 March 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2013.02.006

zbMATH Keywords

eigenvalue problemcompanion matrixChebyshev polynomialsparse polynomialESPRITmatrix pencil factorizationProny polynomialProny-like methodsparse interpolationChebyshev basisrectangular Toeplitz-plus-Hankel matrix

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical interpolation (65D05) Approximation by arbitrary linear expressions (41A45)

Related Items (14)

A new method for Chebyshev polynomial interpolation based on cosine transforms ⋮ Reconstruction of sparse Legendre and Gegenbauer expansions ⋮ Learning algebraic decompositions using Prony structures ⋮ Sparse polynomial interpolation with Bernstein polynomials ⋮ ESPRIT versus ESPIRA for reconstruction of short cosine sums and its application ⋮ Multiscale matrix pencils for separable reconstruction problems ⋮ Mini-workshop: Interpolation, approximation, and algebra. Abstracts from the mini-workshop held February 13--19, 2022 ⋮ The generalized operator based Prony method ⋮ Reconstruction of stationary and non-stationary signals by the generalized Prony method ⋮ Fast ESPRIT algorithms based on partial singular value decompositions ⋮ Sparse sums with bases of Chebyshev polynomials of the third and fourth kind ⋮ On computing the degree of a Chebyshev polynomial from its value ⋮ Rapidly computing sparse Legendre expansions via sparse Fourier transforms ⋮ Sparse interpolation in terms of multivariate Chebyshev polynomials

Cites Work

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• Parameter estimation for nonincreasing exponential sums by Prony-like methods
• Sparse Legendre expansions via \(\ell_1\)-minimization
• On the problem of parameter estimation in exponential sums
• Parameter estimation for exponential sums by approximate prony method
• Early termination in sparse interpolation algorithms
• Representation of sparse Legendre expansions
• On approximation of functions by exponential sums
• Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise
• On sparse reconstruction from Fourier and Gaussian measurements
• A Stable Numerical Method for Inverting Shape from Moments
• Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon Meets Strang–Fix
• CramÉr–Rao Bounds for Multiple Poles and Coefficients of Quasi-Polynomials in Colored Noise
• A new perturbation analysis for signal enumeration in rotational invariance techniques
• Sparse Polynomial Interpolation in Nonstandard Bases
• A generalized Prony method for reconstruction of sparse sums of eigenfunctions of linear operators
• Exponential Data Fitting and its Applications
• Symbolic-numeric sparse interpolation of multivariate polynomials

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