On the stability of unevenly spaced samples for interpolation and quadrature
DOI10.1007/s10543-023-00965-zOpenAlexW4226385732MaRDI QIDQ2697551
Publication date: 12 April 2023
Published in: BIT (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2202.04722
trigonometric interpolationsampling theoryquadratureKadec-1/4 theoremnonuniform discrete Fourier transformation
Trigonometric interpolation (42A15) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Numerical methods for discrete and fast Fourier transforms (65T50) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Numerical quadrature and cubature formulas (65D32) Sampling theory in information and communication theory (94A20)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Sufficient conditions for sampling and interpolation on the sphere
- A generalized sampling theorem for stable reconstructions in arbitrary bases
- Sampling, Marcinkiewicz-Zygmund inequalities, approximation, and quadrature rules
- A fast algorithm for the inversion of general Toeplitz matrices
- Marcinkiewicz-Zygmund inequalities
- Diabetes mellitus modeling and short-term prediction based on blood glucose measurements
- Barycentric formulas for interpolating trigonometric polynomials and their conjugates
- Polynomial interpolation and Marcinkiewicz-Zygmund inequalities on the unit circle
- Fast and stable algorithms for discrete spherical Fourier transforms
- A discrete theory of irregular sampling
- Fast Fourier transforms for nonequispaced data. II
- Efficient numerical methods in non-uniform sampling theory
- Marcinkiewicz-Zygmund-type inequalities, trigonometric interpolation on non-uniform grids and unconditional Schauder bases in Besov spaces on the torus
- A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel
- Uniform error estimates for nonequispaced fast Fourier transforms
- Multivariate Vandermonde matrices with separated nodes on the unit circle are stable
- Worst-case recovery guarantees for least squares approximation using random samples
- Direct inversion of the nonequispaced fast Fourier transform
- Exponential sums with coefficients 0 or 1 and concentrated \(L^p\) norms
- Polynomial interpolation in points equidistributed on the unit circle
- Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature
- The Exponentially Convergent Trapezoidal Rule
- Localized Tight Frames on Spheres
- Extension of Chebfun to Periodic Functions
- The Kadets $1/4$ theorem for polynomials
- Iterative Reconstruction of Multivariate Band-Limited Functions from Irregular Sampling Values
- Fast Fourier Transforms for Nonequispaced Data
- A Nonuniform Fast Fourier Transform Based on Low Rank Approximation
- On Stable Reconstructions from Nonuniform Fourier Measurements
- A Parallel Nonuniform Fast Fourier Transform Library Based on an “Exponential of Semicircle" Kernel
- An Algorithm for the Machine Calculation of Complex Fourier Series
- Trigonometric Interpolation and Quadrature in Perturbed Points
- The evaluation of integrals of periodic analytic functions
- A Class of Nonharmonic Fourier Series
This page was built for publication: On the stability of unevenly spaced samples for interpolation and quadrature