Ten lectures on wavelets
Regular Article: Computing Fourier Transforms and Convolutions on the 2-Sphere
Advances in Applied Mathematics
A spectral embedding method applied to the advection-diffusion equation
Journal of Computational Physics
On the Gibbs Phenomenon and Its Resolution
SIAM Review
Fast algorithms for discrete polynomial transforms
Mathematics of Computation
A comparison of numerical algorithms for Fourier extension of the first, second, and third kinds
Journal of Computational Physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation
SIAM Journal on Numerical Analysis
Asymptotic Fourier Coefficients for a C∞ Bell (Smoothed-“Top-Hat”) & the Fourier Extension Problem
Journal of Scientific Computing
The kink phenomenon in Fejér and Clenshaw–Curtis quadrature
Numerische Mathematik
Journal of Computational Physics
Is Gauss Quadrature Better than Clenshaw-Curtis?
SIAM Review
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We obtain exponentially accurate Fourier series for nonperiodic functions on the interval $[-1,1]$ by extending these functions to periodic functions on a larger domain. The series may be evaluated, but not constructed, by means of the FFT. A complete convergence theory is given based on orthogonal polynomials that resemble Chebyshev polynomials of the first and second kinds. We analyze a previously proposed numerical method, which is unstable in theory but stable in practice. We propose a new numerical method that is stable both in theory and in practice.