Computing discrete convolutions with verified accuracy via Banach algebras and the FFT.

DOI10.21136/AM.2018.0082-18zbMath1488.42047OpenAlexW2803799276WikidataQ129778986 ScholiaQ129778986MaRDI QIDQ1785642

Jean-Philippe Lessard

Publication date: 1 October 2018

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.21136/am.2018.0082-18

zbMATH Keywords

fast Fourier transforminterval arithmetictrigonometric polynomialsFourier coefficientsdiscrete convolutionBanach sequence spacenonlinear Swift-Hohenberg partial differential equation

Mathematics Subject Classification ID

Initial-boundary value problems for higher-order parabolic equations (35K35) Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) General methods in interval analysis (65G40) Numerical methods for discrete and fast Fourier transforms (65T50) Convolution, factorization for one variable harmonic analysis (42A85) Banach sequence spaces (46B45) Fourier series and coefficients in several variables (42B05) Trigonometric polynomials, inequalities, extremal problems (42A05)

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Rigorous numerics for nonlinear heat equations in the complex plane of time ⋮ A rigorous implicit \(C^1\) Chebyshev integrator for delay equations ⋮ Persistence of Periodic Orbits under State-dependent Delayed Perturbations: Computer-assisted Proofs ⋮ Torus knot choreographies in the n-body problem ⋮ Spatial periodic orbits in the equilateral circular restricted four-body problem: computer-assisted proofs of existence

Uses Software

• INTLAB

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